W. Richard Bowen and Nidal Hilal 4

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Preface 

Atomic force microscopy (AFM) was first described in the scientific literature 

in 1986. It arose as a development of scanning tunnelling microscopy 

(STM). However, whereas STM is only capable of imaging conductive 

samples in vacuum, AFM has the capability of imaging surfaces at high 

resolution in both air and liquids. As these correspond to the conditions 

under which virtually all surfaces exist in the real world, this greatly 

increased the potentially useful role of scanning probe microscopies. This 

great potential of AFM led to its very rapid development. By the early 

1990s, it was moving outside of specialist physics laboratories and the first 

commercial instruments were becoming available. 

At the time, our main process engineering research activities were in the 

fields of membrane separation processes and colloid processing. Both of 

these fields involve the manipulation of materials on the micrometre to the 

nanometre length scales. To image the materials used in such processes, we 

used scanning electron microscopy, which was expensive, time-consuming, 

and even more undesirably usually involved complex sample preparation 

procedures and measurement in vacuum which could result in undesirable 

experimental artefacts. Our imagination was fired and our research greatly 

facilitated, following an inspiring lecture given by Jacob Israelachvili at the 

7th International Conference on Surface and Colloid Science in Compiègne, 

France, in July 1991, in which he described some of the very first applications 

of AFM in colloid science. Our first grant application for AFM 

equipment was written very shortly afterwards! 

Since that time there has been an enormous development of the capabilities 

and applicability of AFM. Physicists have devised a bewildering 

range of experimental techniques for probing the different properties 

of surfaces. Scientists, especially those working in the biological sciences, 

have been able to make remarkable discoveries using AFM that would 

have been otherwise unobtainable. A huge amount of scientific literature 

has appeared including a number of introductory and advanced books. 

However, despite the achievements and great potential for the application 

of AFM to process engineering, there is no book-length text describing such 

achievements and applications. Further, the specialist nature of the primary 

literature and the disciplinary strangeness of the existing book-length texts 

can appear rather formidable to engineers who might wish to apply AFM 

ix

x Preface 

in their work. Hence, it is our assessment that the benefit of AFM to 

the development of process engineering is under-fulfilled. Nevertheless, the 

significant decrease in cost of commercial AFM equipment, and its increasing 

‘user-friendliness’, has made the technique readily accessible to most 

engineers. We were, therefore, motivated to put together the present text 

with the specific intention of describing the achievements and possibilities 

of AFM in a way which is directly relevant to the work of our process 

engineering colleagues, with the hope that we will inspire them to apply 

this remarkable technique for the benefit of their own activities. 

We begin in Chapter 1 by providing an outline of the basic principles 

of AFM. The chapter introduces the main features of AFM equipment 

and describes the imaging modes which are most likely to be of benefit in 

process engineering applications. Such knowledge of the main operating 

modes should allow the reader to interpret the nature of the many subtle 

variations described in the primary research literature. We also introduce 

a remarkable benefit of AFM equipment, because it is a force microscope it 

can be used to directly measure surface interactions with very high resolution 

in both force and distance. An especially useful application of this 

capability is the use of ‘colloid probes’, the nature of which is introduced 

and the benefits of which become apparent in several of the later chapters. 

AFM can generate beautiful images of surfaces at subnanometre resolution. 

However, the detailed interpretation of the features of such images 

can benefit greatly from an understanding of the fundamental interactions 

from which they arise. This is the subject of Chapter 2. Depending on the 

materials being investigated and the experimental conditions, the interactions 

which give rise to such images, either separately or simultaneously, 

include van der Waals forces, electrical double layer forces, hydrophobic 

interactions, solvation forces, steric interactions, hydrodynamic drag forces 

and adhesion. AFM also has the capability to quantify such interactions, 

especially using colloid probe techniques. For this reason, mathematical 

descriptions of such interactions are given in forms which have proved 

of practical use in process engineering. 

Once the basics of AFM have been outlined, it is possible to move to 

a description of specific applications. Process engineering is a diverse 

and growing field comprising both established processes of great societal 

significance and new areas of huge promise. We begin in Chapter 3 

by describing investigations of an established and important type of 

phenomenon – the quantification of particle–bubble interactions. Such 

interactions are of fundamental significance in some of the largest-scale 

industrial processes, most notably in mineral processing and in wastewater 

treatment. It is especially the capability of AFM equipment to quantify the 

interactions between bubbles and micrometre size particles that can lead to 

the development of processes of increased flotation efficiency and greater 

specificity of separation. This is a remarkable example of how nanoscale 

interactions control the efficiency of megascale processes.

Preface xi 

Membrane separation processes are one of the most significant developments 

in process engineering in recent times. They now find widespread 

application in fields as diverse as water treatment, pharmaceutical processing, 

food processing, biotechnology, sensors and batteries. Membranes 

are most usually thin polymeric sheets, having pores in the range from 

the micrometre to subnanometre, that act as advanced filtration materials. 

Their separation capabilities are due to steric effects and the whole range 

of interactions that can be probed by AFM. Hence, there is a very close 

match between the factors that control the effectiveness of a membrane 

process and the measurement capabilities of AFM. In Chapter 4, we provide 

a survey of the numerous ways in which AFM can be used to study 

the factors controlling membrane processes. We consider both advanced 

imaging and force measurement techniques, and how they may be combined, 

for example, to provide a ‘visualisation’ of the rejection of a colloid 

particle by a membrane pore. Chapter 5 is more especially concerned with 

the use of AFM in the development of new membranes with specifically 

desirable properties. We focus, in particular, on the development of fouling 

resistant membranes, i.e. membranes with the minimum of unwanted 

adhesion of substances from the fluids being processed. 

In the pharmaceutical industry, there is an increasing drive to develop 

new ways of drug delivery, both means for the presentation of drugs to 

the patient and of drug formulations which target specific sites in the 

body. Both of these goals can benefit from knowledge of structures and 

interactions at the nanoscale. Thus, pharmaceutical development can 

benefit from both the imaging and force measurement capabilities of 

AFM, as described in Chapter 6. The colloid probe, or more precisely 

drug particle probe, techniques are again very important in this work. 

However, there is also scope for the use of advanced techniques, such 

as micro- and nanothermal characterisation using a scanning thermal 

microscope (SThM), which can provide spatial information at a resolution 

unavailable to conventional calorimetry. 

Bioprocessing is acquiring a sophistication that was unimaginable even 

a few years ago. An important example is given in Chapter 7. Cells sense 

and respond to their surrounding microenvironment. The chapter reviews 

the application of micro/nanoengineering and AFM to the investigation 

of cell response in engineered microenvironments that mimic the natural 

extracellular matrix. In particular, the chapter reports the use of micro/ 

nanoengineering to make structures that aid the understanding of fundamental 

cellular interactions, which in turn help further development of 

new therapeutic methods. Specific attention is given to the combination 

of AFM with optical microscopy for the simultaneous interrogation of 

biophysical and biochemical cellular processes and properties, as well as 

the quantification of cell viscoelasticity. 

Throughout the process industries, and more generally in manufacturing, 

the surfaces of materials are modified with coatings to protect

xii Preface 

them from hostile conditions and to functionalise them for a variety of 

purposes. In particular, ultrathin coatings play a crucial role in many 

processes, ranging from protection against chemical corrosion to microfabrication 

for microelectronics and biomedical devices. Chapter 8 

describes the use of AFM for the study of the fine structure and local 

nanomechanical properties of such advanced polymer monolayers and 

submonolayers. AFM allows the real-time/real-space monitoring of relevant 

physicochemical surface processes. As miniaturisation of electronic 

and medical devices approaches the nanometre scale, AFM is becoming 

the most important characterisation tool of their nanostructural and 

nanomechanical properties. 

AFM has been considered primarily as a technique for the investigation 

of the surfaces of solid materials, with the considerable benefit that 

it can be used to carry out such investigations in liquid environments. 

However, AFM may also be used to study the properties of such liquids 

themselves. This is the topic of Chapter 9, which describes dynamic studies 

of confined fluids, micro- and nanorheology, cavitation and adhesive 

failure in thin films, and meso-scale experimental studies of the tensile 

behaviour of thin fluid films. Such studies benefit considerably from the 

coupling of AFM with high-magnification optical microscopy and highspeed 

video techniques. The development of such studies may be of considerable 

importance for the many large-scale processes that depend on 

the properties of thin liquid films, and also for instances where the available 

quantities of fluids are tiny, such as for synovial fluid. 

In the final chapter, we have pooled the thoughts of the contributors 

to provide a vision of some of the ways in which AFM may contribute to 

the development of process engineering in the future. 

We thank all of the authors who have collaborated in the writing of 

this volume. We are very grateful for their willingness to devote time to 

this task and for their timely delivery of high-quality manuscripts. We 

also thank the many colleagues and research students who have contributed 

to the work described. Particular thanks are due to Dr Peter 

M. Williams. Peter worked as a research technician at our centre when 

we first started AFM studies. The results of our research as presented in 

this volume owe much to his technical ingenuity and patience. 

W. Richard Bowen and Nidal Hilal 

wrichardbowen@i-newtonwales.org.uk 

nidal.hilal@nottingham.ac.uk 

Wales and England 

February 2009

About the Editors 

Professor W. Richard Bowen is a Fellow of the UK Royal Academy of 

Engineering. His work in chemical and biochemical engineering is widely 

recognised as world leading, particularly in the application of atomic force 

microscopy and in the development of membrane processes. He holds 

chairs in the Schools of Engineering at the University of Wales Swansea 

and the University of Surrey. He has carried out extensive consultancy for 

industry, government departments, research councils and universities on 

an international basis, currently through i-NewtonWales. 

xiii

xiv About thE Editors 

Professor Nidal Hilal is a Fellow of the Institution of Chemical Engineers 

and currently the Director of the Centre for Clean Water Technologies 

at the University of Nottingham. He obtained a PhD in Chemical 

Engineering from the University of Wales in 1988. Over the years, he has 

made a major contribution becoming an internationally leading expert in 

the application of Atomic Force Microscopy in process engineering and 

membrane technology. Professor Hilal is the author of over 300 refereed 

publications, including 4 textbooks and 11 invited chapters in international 

handbooks. In recognition of his substantial and sustained contribution 

to scientific knowledge, he was awarded a senior doctorate, Doctor 

of Science (DSc), from the University of Wales and the Kuwait Prize for 

Water Resources Development in 2005. He is a member of the editorial 

boards for a number of international journals and an advisor for international 

organizations including the Lifeboat Foundation. He is also on the 

panel of referees for the UK and international Research Councils. 

Professor Hilal acknowledges His Majesty King Abdullah Bin Abdul 

Aziz Al-Saud of Saudi Arabia, who is a keen advocate for nanotechnology 

and process engineering, particularly in the field of desalination and 

water research for the benefit of all humanity.

List of Contributors 

Prof. W. Richard Bowen, FREng 

i-NewtonWales, 54 Llwyn y mor, Caswell, Swansea, SA3 4RD, UK 

wrichardbowen@i-newtonwales.org.uk 

Prof. Nidal Hilal, DSc 

Director of Centre for Clean Water Technologies, Faculty of Engineering, 

University of Nottingham, University Park, Nottingham NG7 2RD, UK 

nidal.hilal@nottingham.ac.uk 

Prof. Clive J. Roberts 

Director of Nottingham Nanotechnology and Nanoscience Centre, University 

of Nottingham, Nottingham NG7 2RD, UK 

clive.roberts@nottingham.ac.uk 

Dr Huabing Yin 

Department of Electronic and Electrical Engineering, University of Glasgow, 

Glasgow, UK 

hy@elec.gla.ac.uk 

Dr Vasileios Koutsos 

Institute for Materials and Processes, School of Engineering and Centre for 

Materials Science & Engineering, The University of Edinburgh, The King’s 

Buildings, Edinburgh EH9 3JL, UK 

vasileios.koutsos@ed.ac.uk 

Prof. P. Rhodri Williams 

Multidisciplinary Nanotechnology Centre, School of Engineering, Swansea 

University, Singleton Park, Swansea SA2 8PP, UK 

p.r.williams@swansea.ac.uk 

Dr Paul Melvyn Williams 



paul.melvyn.williams@swansea.ac.uk 

Dr Matthew Barrow 



m.s.barrow@swansea.ac.uk 

xv

xvi List of Contributors 

Dr Daniel Johnson 

Centre for Clean Water Technologies, Faculty of Engineering, The University 

of Nottingham, University Park, Nottingham, NG7 2RD, UK 

daniel.johnson@nottingham.ac.uk 

Gordon McPhee 

Department of Electronic and Electrical Engineering, University of 

Glasgow, UK 

gmcphee@elec.gla.ac.uk 

Dr Phil Dobson 

Department of Electronic and Electrical Engineering, University of 

Glasgow, UK 

pdobson@elec.gla.ac.uk

C H A P T E R 

Basic Principles of Atomic 

Force Microscopy 

Daniel Johnson, Nidal Hilal and 

W. Richard Bowen 

O U T L I N E 

. Introduction 2 

.2 The atomic force microscope 3 

.3 Cantilevers and probes 6 

1.3.1 Effect of Probe Geometry 7 

.4 Imaging modes 8 

1.4.1 Contact Mode Imaging 9 

1.4.2 Intermittent Contact (Tapping) Mode 10 

1.4.3 Non-Contact Mode 10 

1.4.4 Force Volume Imaging 11 

1.4.5 Force Modulation Mode 12 

1.4.6 Lateral/Frictional Force Mode 12 

.5 The afm as a force sensor 2 

.6 Calibration of afm microcantilevers 6 

1.6.1 Calibration of Normal spring Constants 16 

1.6.2 Calibration of Torsional and Lateral spring Constants 21 

.7 Colloid probes 22 

abbreviations and symbols 23 

References 24 

Atomic Force Microscopy in Process Engineering © 2009, Elsevier Ltd

2 1. BAsIC PRINCIPLEs OF ATOMIC FORCE MICROsCOPy 

. InTroduCTIon 

The atomic force microscope (AFM), also referred to as the scanning 

force microscope (SFM), is part of a larger family of instruments termed 

the scanning probe microscopes (SPMs). These also include the scanning 

tunnelling microscope (STM) and scanning near field optical microscope 

(SNOM), amongst others. The common factor in all SPM techniques is 

the use of a very sharp probe, which is scanned across a surface of interest, 

with the interactions between the probe and the surface being used 

to produce a very high resolution image of the sample, potentially to the 

sub-nanometre scale, depending upon the technique and sharpness of 

the probe tip. In the case of the AFM the probe is a stylus which interacts 

directly with the surface, probing the repulsive and attractive forces 

which exist between the probe and the sample surface to produce a highresolution 

three-dimensional topographic image of the surface. 

The AFM was first described by [1]Binnig et al. as a new technique 

for imaging the topography of surfaces to a high resolution. It was created 

as a solution to the limitations of the STM, which was able to image 

only conductive samples in vacuum. Since then the AFM has enjoyed 

an increasingly ubiquitous role in the study of surface science, as both 

an imaging and surface characterisation technique, and also as a means 

of probing interaction forces between surfaces or molecules of interest 

by the application of force to these systems. The AFM has a number of 

advantages over electron microscope techniques, primarily its versatility 

in being able to take measurements in air or fluid environments rather 

than in high vacuum, which allows the imaging of polymeric and biological 

samples in their native state. In addition, it is highly adaptable 

with probes being able to be chemically functionalised to allow quantitative 

measurement of interactions between many different types of 

materials – a technique often referred to as chemical force microscopy. 

At the core of an AFM instrument is a sharp probe mounted near to 

the end of a flexible microcantilever arm. By raster-scanning this probe 

across a surface of interest and simultaneously monitoring the deflection 

of this arm as it meets the topographic features present on the surface, 

a three-dimensional picture can be built up of the surface of the sample 

to a high resolution. Many different variations of this basic technique 

are currently used to image surfaces using the AFM, depending upon 

the properties of the sample and the information to be extracted from it. 

These variations include ‘static’ techniques such as contact mode, where 

the probe remains in constant contact with the sample, and ‘dynamic’ 

modes, where the cantilever may be oscillated, such as with the intermittent 

or non-contact modes. The forces of interaction between the probe 

and the sample may also be measured as a function of distance by the

1.2 THE ATOMIC FORCE MICROsCOPE 3 

monitoring of the deflection of the cantilever, providing that the spring 

constant of the lever arm is sufficiently calibrated. 

In this chapter the basic principles of operation of an AFM will be presented, 

outlining the most common imaging modes and describing the 

acquisition of force distance measurements and techniques to calibrate 

cantilever spring constants. 

.2 The aTomIC forCe mICrosCope 

In Figure 1.1 the basic set-up of a typical AFM is shown. Cantilevers 

are commonly either V-shaped, as shown, or a rectangular, ‘diving 

board’ shaped. The cantilever has at its free end a sharp tip, which acts 

as the probe of interactions. This probe is most commonly in the form 

of a square-based pyramid or a cylindrical cone. A few examples of different 

configurations for levers and probes are shown in Figure 1.2. 

Commercially manufactured probes and cantilevers are predominantly 

of silicon nitride (the formula normally given for silicon nitride is Si 3N 4, 

although the precise stoichiometry may vary depending on the manufacturing 

process) or silicon (Si). Typically the upper surface of the cantilever, 

opposite to the tip, is coated with a thin reflective surface, usually of 

either gold (Au) or aluminium (Al). 

The probe is brought into and out of contact with the sample surface 

by the use of a piezocrystal upon which either the cantilever chip or the 

surface itself is mounted, depending upon the particular system being 

Photodetector 

A B 

Sample surface 

C D 

Light path 

Probe 

Light source 

y 

Chip 

Cantilever 

fIgure . Basic AFM set-up. A probe is mounted at the apex of a flexible Si or Si 3N 4 

cantilever. The cantilever itself or the sample surface is mounted on a piezocrystal which 

allows the position of the probe to be moved in relation to the surface. Deflection of the 

cantilever is monitored by the change in the path of a beam of laser light deflected from the 

upper side of the end of the cantilever by a photodetector. As the tip is brought into contact 

with the sample surface, by the movement of the piezocrystal, its deflection is monitored. 

This deflection can then be used to calculate interaction forces between probe and sample. 

z 

x


A B 

C D 

fIgure .2 Example of SEM images of different probes and cantilever types. 

A: pyramidal probe; B: conical high aspect ratio probe for high resolution imaging; C: two 

V-shaped cantilevers for contact mode imaging; D: chip with a series of beam-shaped levers 

of different lengths. In this case the levers are tipless to allow mounting of particles of interest 

for force measurements. 

used (these two configurations are referred to as tip-scanning or surfacescanning, 

respectively). Movement in this direction is conventionally 

referred to as the z-axis. A beam of laser light is reflected from the reverse 

(uppermost) side of the cantilever onto a position-sensitive photodetector. 

Any deflection of the cantilever will produce a change in the position of 

the laser spot on the photodetector, allowing changes to the deflection to 

be monitored. The most common configuration for the photodetector is 

that of a quadrant photodiode divided into four parts with a horizontal 

and a vertical dividing line. If each section of the detector is labelled A 

to D as shown in Figure 1.1, then the deflection signal is calculated by 

the difference in signal detected by the A � B versus C � D quadrants. 

Comparison of the signal strength detected by A � C versus B � D 

will allow detection of lateral or torsional bending of the lever. Once 

the probe is in contact with the surface, it can then be raster-scanned 

across the surface to build up relative height information of topographic 

features of the sample.

Force 

1.2 THE ATOMIC FORCE MICROsCOPE 5 

Intermittent 

contact mode 

Contact mode 

Distance 

Repulsion 

Non-contact mode 

Attraction 

fIgure .3 Diagram illustrating the force regimes under which each of the three most 

common AFM imaging modes operate. Contact mode operation is in the repulsive force 

regime, where the probe is pressed against the sample surface, causing an upwards deflection 

of the cantilever. Non-contact mode interrogates the long-range forces experienced 

prior to actual contact with the surface. With intermittent contact, or tapping mode, the 

probe is oscillated close to the surface where it repeatedly comes into and out of contact 

with the surface. 

This ‘optical lever’ method to detect deflection of the cantilever is the 

method primarily in use currently [2, 3]. However, the original design 

for the AFM used an STM piggy-backed onto the upper side of the AFM 

as a deflection sensor [1]. Whilst this allowed extremely accurate determination 

of the deflection, it also could detect deflection only within a 

very small range, which is insufficient for most purposes. In addition, 

other methods have been trialled in the past for this purpose including 

the measurement of optical interferometry effects [4] as well as fabricating 

levers to be able to detect deflection through a piezoresistance-based 

mechanism [5–14]. 

Scanners are available in different configurations, depending upon 

the particular AFM employed, or the purpose for which it is required. 

Tube scanners consist of a hollow tube made of piezoceramic material. 

Depending on how electrical current is applied, the tube may extend in 

the z-direction or be caused to flex in either the x- or y-direction to facilitate 

scanning. Alternatively scanners may consist of separate piezocrystals 

for each movement direction. Such a configuration removes certain 

non-linearity problems, which may occur in the simpler tube scanners. 

In many commercially available AFMs, especially in older models, the 

movement in the x- and y-directions may be achieved by the movement 

of the sample rather than by the movement of the probe.


.3 CanTIlevers and probes 

Depending upon the uses required and the forces which may act upon 

them, cantilevers may be chosen from a large range available. Most microcantilevers 

used in AFMs are produced from monolithic Si 3N 4 or Si using 

micromachining techniques developed in the semi-conductor industry [9, 

15–20]. These two materials are used extensively due to the high suitability 

of their mechanical properties such as high yield strengths and elastic moduli 

[21–24]. Applications where high forces are experienced require stiff 

levers with probes resistant to deformation. On the contrary, where low 

forces are experienced or when samples are soft and easily deformed, levers 

with low force constants are required for both the increased force sensitivity 

at low forces and avoiding deforming or damaging samples. In addition to 

these silicon-based cantilevers and probes, the literature describes a number 

of other materials which have been utilised in the production of AFM 

levers. These include the production of diamond tips integrated into silicon 

levers [25, 26] or fabricated diamond levers [27], particularly useful where 

the probe tip may be subject to very high pressures at the apex, such as during 

nano-indentation measurements; quartz ‘tuning fork’ levers with polymeric 

tips for dynamic imaging modes [28]; metal wires, such as tungsten, 

as levers [4, 29, 30]; as well as more exotic materials [31, 32]. In addition, 

ultrasharp probes with very high aspect ratios can be manufactured by the 

growing of Si ‘whiskers’ on the apex of the probe to improve the resolution 

of samples with rough surfaces due to their relatively high aspect ratio [33, 

34]. In addition, a large amount of work is being undertaken to investigate 

the attachment of carbon nanotubes to the apex of cantilever tips to act as 

ultrasharp probes. Carbon nanotubes have diameters typically in the range 

of 1–20 nm and a very high aspect ratio making them ideal, providing that 

they can be attached in a robust and predictable manner [35–39]. 

Another topic which must be considered when undertaking AFM 

measurements is the presence of contaminants on the probe, particularly 

at the tip. Commercially bought probes are placed on a sticky polymer 

surface, such as polydimethylsiloxane (PDMS), in plastic boxes and as a 

result tend to be coated in a hydrophobic contaminant layer [40]. In addition 

to this, once removed from packaging, the probes are likely to suffer 

exposure to airborne organic contaminants with the likelihood of exposure 

increasing over time. This can have a significant effect on imaging 

resolution, which depends to a great extent on the radius of curvature 

of the probe tip being as small as possible. Even the presence of a small 

amount of contamination could increase this significantly. It has also been 

observed that the presence of a contamination layer can increase the measured 

adhesion values between a probe and surface under ambient conditions 

[41]. The resultant increased forces between probe and sample will

also increase the effective area of contact, further decreasing the resolution 

of images. The presence of a contaminant layer can also adversely affect 

any attempt to chemically functionalise probes, preventing formation of 

an even layer of the desired coating material. There are various methods 

available to successfully clean AFM probes, which will now be described. 

Technologically, the simplest method is chemical cleaning by immersing 

the probe in an acid peroxide solution – most commonly a mixture 

referred to as piranha solution (usually a 7:3 ratio by volume of concentrated 

H 2SO 4 and 30% v/v H 2O 2, although the proportions may vary 

between laboratories) for a short period of time, which has been verified 

as effective in removing organic surface contaminants and increasing the 

hydrophilicity of the levers, although inorganic contaminants are not 

affected [42, 43]. This mixture is used in the semiconductor industry to 

clean photoresist and other contaminants from silicon wafers [44]. Simple 

cleaning by rinsing with organic solvents is insufficient to remove all the 

organic contaminants [43]. Piranha solution is extremely reactive with any 

organic material and can remove contaminants from levers and silicon 

surfaces in a very short space, with necessary exposure times to remove 

contaminants from AFM probes, which is typically less than 1 min. 

However, for this reason it is very corrosive if it comes into contact with 

any biological material including skin and must be handled with great 

care by the user. In addition if it comes into contact with a relatively large 

quantity of organic material, such as by allowing to mix with organic solvents, 

the mixture may become explosive, posing a significant danger to 

laboratory users, with accounts of such laboratory accidents extant in the 

literature [45, 46]. As such, this method is not recommended if other safer 

cleaning methods are available and only small volumes should be produced 

at a time as and when required. Another commonly used method 

to clean AFM probes is to use ultraviolet (UV) light [47, 48]. This works 

by converting oxygen to form small amounts of ozone, which is then further 

broken down to produce highly reactive singlet oxygen, which in 

turn reacts with organic contaminant materials on the surfaces. For greater 

effectiveness, such a system is often combined with an independent ozone 

source to increase the amount of singlet oxygen radicals produced. Many 

laboratories also use plasma ashing or etching processes to remove contaminants 

from probes and samples [41, 42, 48–50], which has been demonstrated 

to be particularly effective in the removal of thin layers of organic 

contamination. Here a process gas, usually oxygen or argon, is ionised 

under a partial vacuum in a chamber containing the sample to be cleaned. 

.3. effect of probe geometry 

1.3 CANTILEvERs ANd PROBEs 7 

Because all measurements made using an AFM are based upon the 

physical interaction between the probe and the sample, it follows that the


shape of the probe is of fundamental importance in determining those 

interactions. In addition to the radius of curvature at the apex of the 

probe, the geometry of all of the parts of the probe which can interact 

with the sample are of great importance, particularly when imaging or 

performing indentation measurements. 

When imaging a sample surface, features of greatly varying geometry 

may be encountered. The ability to resolve these features depends 

upon both the sharpness of the probe tip and the aspect ratio of the 

probe. First, the probe sample contact area is a limit to AFM resolution. 

This is dependent not just upon the sharpness of the probe tip, 

but also upon the force with which the probe presses into the surface 

and the consequent mechanical deformations induced in the probe 

and sample. As the sample is deformed, the probe tip will become 

indented into the sample and a greater part of the probe surface will be in 

direct contact with the sample. Conversely if it presses against a hard 

sample with sufficient force, the probe itself may become deformed, 

similarly contributing to an increased interaction area. This interaction 

will be dependent upon the shape of the probe as well as purely on the 

radius of curvature found at the apex. Features present upon the surface 

which are smaller in size than the contact area will be unable to be 

successfully resolved. 

When asperities, which are sharper than the probe, on the surface are 

encountered, the image of the feature which is obtained will be based 

more upon the shape of the probe than upon the surface feature [51, 52] 

due to convolution effects. This is a problem potentially arising in all 

forms of SPM. This may be commonly observed when low aspect ratio 

probes are scanned over surfaces with high aspect ratio asperities. In 

effect the probe is imaged by the surface. A similar effect may be seen 

when the probe encounters a step edge on the sample, which is steeper 

than the side of the probe. In this case a broadening effect will occur 

where the feature under observation will appear to be wider than it actually 

is. These convolution effects serve to produce images which rather 

than being true representations of sample topography represent a composite 

of the topographies of both sample and probe. The finer the tip 

and higher the aspect ratio of the probe, will provide images which are 

a truer representation of the real topography of the sample. 

.4 ImagIng modes 

There are many different imaging modes available for the AFM, providing 

a range of different information about the sample surfaces being 

examined. However, for simplicity the most common modes will be 

considered here. In Figure 1.3 the force regimes under which the main

imaging modes occur are illustrated schematically. In this figure the 

interaction forces are sketched as the probe approaches and contacts the 

surface, with distance increasing to the right. At large separations there 

are no net forces acting between the probe and the sample surface. As 

probe and surface approach each other, attractive van der Waals interactions 

begin to pull the probe towards the surface. As contact is made, 

the net interaction becomes repulsive as electron shells in atoms in the 

opposing surfaces repel each other. In this figure, the repulsive forces are 

shown as being positive and attractive forces negative. 

.4. Contact mode Imaging 

1.4 IMAgINg MOdEs 

Contact mode imaging is so called because the probe remains in contact 

with the sample at all times. As a result, the probe–sample interaction 

occurs in the repulsive regime as illustrated in Figure 1.3. This is the 

simplest mode of AFM operation and was that originally used to scan 

surfaces in early instruments. There are two variations on this technique: 

constant force and variable force. With constant force mode, a feedback 

mechanism is utilised to keep the deflection, and hence force, of the 

cantilever constant. As the cantilever is deflected the z-height is altered 

to cause a return to the original deflection or ‘set point’. The change in 

z-position is monitored and this information as a function of the x,y- 

position is used to create a topographical image of the sample surface. 

For variable force imaging, the feedback mechanisms are switched off so 

that z-height remains constant and the deflection is monitored to produce 

a topographic image. This mode can be used only on samples which are 

relatively smooth with low lying surface features, but for surfaces to 

which it is applicable, it can provide images with a sharper resolution 

than constant force mode. 

Contact mode is often the mode of choice when imaging a hard and 

relatively flat surface due to its simplicity of operation. However, there 

are several drawbacks. Lateral forces can occur when the probe traverses 

steep edges on the sample, which may cause damage to the probe or 

the sample, or also result from adhesive or frictional forces between the 

probe and the sample. This can also lead to a decrease in the resolution of 

images due to the ‘stick-slip’ movement of the probe tip over the surface. 

In addition, the relatively high forces with which the probe interacts with 

the sample can cause deformation of the sample, leading to an underestimation 

of the height of surface features, as well as causing an increase in 

the area of contact between the probe and the surface. The area of contact 

between the probe and the surface sets a limit to the resolution which 

can be achieved. Where a soft, and therefore easily deformable and easily 

damaged, sample is to be imaged, dynamic modes of imaging, such as 

intermittent contact or non-contact modes, are usually preferable.


.4.2 Intermittent Contact (Tapping) mode 

In order to overcome the limitations of contact mode imaging as mentioned 

earlier, the intermittent, or tapping, mode of imaging was developed 

[53–55]. Here the cantilever is allowed to oscillate at a value close 

to its resonant frequency. When the oscillations occur close to a sample 

surface, the probe will repeatedly engage and disengage with the surface, 

restricting the amplitude of oscillation. As the surface is scanned, 

the oscillatory amplitude of the cantilever will change as it encounters 

differing topography. By using a feedback mechanism to alter the 

z-height of the piezocrystal and maintain a constant amplitude, an image 

of the surface topography may be obtained in a similar manner as with 

contact mode imaging. In this way as the probe is scanned across the surface, 

lateral forces are greatly reduced compared with the contact mode. 

When using tapping mode in air, capillary forces due to thin layers of 

adsorbed water on surfaces, as well as any other adhesive forces which 

may be present, have to be overcome. If the restoring force of the cantilever 

due to its deflection is insufficient to overcome adhesion between 

the probe and the surface, then the probe will be dragged along the surface 

in an inadvertent contact mode. As a result, for this mode in air the 

spring constants of AFM cantilevers are by necessity several orders of 

magnitude greater than those used for either tapping mode in liquid or 

contact mode (typically in the range of 0.01–2 Nm �1 for contact mode to 

20–75 Nm �1 for tapping in air). 

As surfaces with different mechanical and adhesive properties are 

scanned, the frequency of oscillation will change, causing a shift in the 

phase signal between the drive frequency and the frequency with which 

the cantilever is actually oscillating [56, 57]. This phenomenon has been 

used to produce phase images alongside topographic images, which are 

able to show changes in the material properties of the surfaces being 

investigated. However, whilst the qualitative data provided by the phase 

images are useful, it is difficult to extract quantitative information from 

them because they are a complex result of a number of parameters including 

adhesion, scan speed, load force, topography and the material, especially 

elastic, properties of the sample and probe [57, 58]. 

.4.3 non-Contact mode 

In non-contact mode imaging, the cantilever is again oscillated as in 

intermittent contact mode, but at much smaller amplitude. As the probe 

approaches the sample surface, long-range interactions, such as van der 

Waals and electrostatic forces, occur between atoms in the probe and the 

sample. This causes a detectable shift in the frequency of the cantilever’s

oscillations. Detection of the shift in phase between the driving and oscillating 

frequencies allows the z-positioning of the cantilever to be adjusted 

to allow the cantilever to remain out of contact with the surface by the 

operation of a feedback loop [59]. Because the probe does not contact the 

surface in the repulsive regime, the area of interaction between the tip 

and the surface is minimised allowing potentially for greater surface resolution. 

As a result in this mode, it is imaging which is best able to achieve 

true atomic resolution, when examining a suitable surface under suitable 

conditions. However, in practice obtaining images of a high quality is a 

more daunting prospect than intermittent contact mode. When imaging 

in air all but the most hydrophobic regions of surfaces will have a significant 

water layer, which may be thicker than the range of the van der 

Waals forces being probed. This combined with the low oscillation amplitude 

will mean that the probe will be unable to detach from the water 

layer easily, degrading imaging resolution. 

.4.4 force volume Imaging 

1.4 IMAgINg MOdEs 

The force volume imaging mode is a combination of conventional 

imaging with the measurement of force distance curves (see Section 2.2 

for explanation of these measurements). For each pixel of the image, a 

force distance curve is obtained by bringing the probe into and then out 

of contact with the surface and simultaneously recording the deflection 

of the lever as a function of the z-directional translation, so that concurrently 

with obtaining a conventional topographic (height) image, information 

about how interaction forces between the probe and the sample 

vary with the sample topography is obtained. By plotting an image 

scaled to show the lowest force value for each pixel, an adhesion map of 

the surface can be obtained [60]. This is useful for highlighting different 

adhesive properties of different surface domains [60–62], which can be 

particularly useful if the probe itself carries a tailored chemical functionality 

[63, 64]. In addition plots of the relative elasticity of different surface 

domains can be produced, if working with sufficiently soft samples 

such as polymer layers [65] or surface immobilised cells [63]. Where force 

measurements are to be obtained between the probe and a relatively 

rough surface, a high variability between curves may be observed due 

to surface asperities, causing a great variation in the contact area from 

one point to another. If this is the case then the force volume mode is a 

useful way to obtain the large numbers of force curves needed over an 

area. As obtaining a large number of force curves at the same time is very 

memory intensive, force volume images are typically lower in resolution, 

in terms of the number of pixels in an image than the images obtained in 

other AFM modes.


.4.5 force modulation mode 

Force modulation mode combines some of the aspects of both contact 

and dynamic modes of imaging. During the operation of the force 

modulation mode of AFM, either the cantilever or the sample is oscillated 

sinusoidally in the z-direction, while raster-scanning the probe 

across the sample surface whilst in constant contact [66–70]. The amplitude 

and phase of these oscillations is monitored simultaneously with 

the creation of a topographic image of the surface. This allows changes in 

the mechanical compliance of the surface to be monitored and compared 

with changes in the topography. From the knowledge of the stiffness of 

the cantilever, the geometry of the probe apex and its area of contact with 

the sample and the utilisation of an appropriate contact mechanics model 

such as the Hertz or the Johnson, Kendall and Roberts (JKR) models, it 

is possible to extract useful quantitative information about the material 

properties of the surface, such as the elastic modulus. The ability of this 

technique to monitor differences in the surface mechanical properties 

between different domains of surfaces to the high resolution obtainable 

with the AFM is of much use in the characterisation of materials engineered 

on the nano-scale. 

.4.6 lateral/frictional force mode 

In lateral force mode, the forces exerted upon the probe tip in the lateral 

(x) direction as it is scanned across a surface are recorded simultaneously 

with topography. This is of particular interest for obtaining 

quantitative measurements of the frictional forces felt between the probe 

and the sample [29, 30, 71–74] and of much interest in the field of nanotribology, 

where the frictional and wearing properties of materials used to 

construct micro-machines is of great importance due to their high surface 

area to volume ratio. To extract quantitative data from the measurements, 

a number of variables need to be accounted for, such as the normal force 

applied by the probe tip, the lateral spring constant of the cantilever (see 

Section 1.4.2), the geometry of the tip apex (particularly its area of contact 

with the surface) and the sensitivity of the optical lever to the torsional 

bending of the lever arm. 

.5 The afm as a forCe sensor 

One of the major applications of the AFM is in the quantitative measurement 

of interaction forces between either the probe tip, or an attached 

particle replacing the tip, and a sample surface. This technique has been 

employed to examine a wide variety of systems including the mechanical

1.5 THE AFM As A FORCE sENsOR 3 

properties of materials on the micro- and nano-scales [75–80] of interest 

for characterising nano-engineered materials; adhesion between surfaces 

[80–85]; attractive and repulsive surface forces, such as van der Waals and 

electrostatic double layer forces [86–89] both of interest when studying 

the properties of colloidal particles; and to probe the mechanical properties 

and kinetics of bond strength of biomolecules [90–93]. 

As the tip of the cantilever is brought into and out of contact with a 

surface, a force curve is generated, describing the cantilever deflection 

(or force) as a function of distance. A typical force curve is illustrated in 

Figure 1.4. Raw data are plotted as displacement of the z-piezo on the 

abscissa, whilst cantilever deflection is plotted as the signal on the photodetector 

(commonly either as voltage V or sometimes as current A) 

on the ordinate. As the cantilever begins its approach (described by the 

red trace), it is away from the surface and hence there is no detection of 

change in force (point 1 in the figure) – the cantilever is said to be at its 

‘free level’, i.e. at this point there are no net forces acting on it (assuming 

that the probe is not travelling fast enough for hydrodynamic drag 

forces to have a significant effect). As the probe comes into close proximity 

with the cantilever, long-range forces may cause interaction between 

the probe and the objective surface. Repulsive forces will cause the lever 

to deflect upwards and away from the surface, whereas attractive forces 

will deflect the lever downwards, towards the surface. If the gradient of 

attractive forces is less than the stiffness of the lever, then the probe will 

momentarily be deflected downwards, before re-equilibrating at its free 

level due to the restoring force stored in the lever. If the probe reaches 

a point where the gradient of attractive forces exceeds the stiffness of 

the cantilever, then the cantilever will be rapidly deflected downwards 

allowing the probe to touch the surface in a ‘snap-in’ or ‘jump-to- 

contact’. In the absence of attractive surface forces, this jump-to-contact 

will not be seen. When the cantilever makes hard contact with the surface, 

it is deflected upwards due to repulsion between electron shells of 

atoms in the opposing material surfaces, and a positive force is observed 

(point 2). The cantilever is then retracted and initially follows the path 

of the approach trace in the contact region. The cantilever often remains 

attached to the surface by adhesive forces which results in a downwards 

deflection of the cantilever as the probe retracts away from the surface, 

causing a hysteresis between the trace and the retrace. Eventually the 

separation force becomes sufficient to overcome the adhesion between 

the probe tip and the surface, and the cantilever snaps back to its initial 

free level position (point 3). 

This behaviour results in a curve of deflection (measured as raw signal) 

versus displacement of the piezo in the z-direction. When the surface 

being pressed against is hard and does not undergo significant deformation, 

the z-movement will be equal to the deflection of the cantilever. As a


Deflection (nA) 

A 

Force (nN) 

B 

60 

50 

40 

30 

20 

10 

0 

0 50 100 150 200 250 300 350 400 

–10 

–20 

–30 

35 

30 

25 

20 

15 

10 

5 

0 

–100 –50 0 50 100 150 200 250 300 

–5 

–10 

2. 

z-piezo translation (nm) 

Distance (nm) 

fIgure .4 An example of force curve. Raw data are shown in (a) plotted as displacement 

of the z-piezo versus deflection as measured on the photosensitive detector. 

Calculation of the cantilever stiffness and sensitivity of the optical lever set-up allow the 

raw data to be converted into probe–sample separation distance versus the force, with converted 

force curve shown in (b). By convention, for AFM force curves, attractive forces are 

portrayed as negative and repulsive forces as positive. 

3. 

1.

1.5 THE AFM As A FORCE sENsOR 5 

consequence, the slope obtained from contact with an unyielding surface 

provides the sensitivity of the optical lever system. By dividing the raw 

deflection data by this sensitivity value, it can be converted into an actual 

deflection distance. This sensitivity value is essential for the calculation 

of force values from raw deflection data. This deflection value (distance) 

can also then be subtracted from the z-piezo displacement to give the 

actual distance travelled by the probe. An alternative method of finding 

the optical lever sensitivity without needing to make hard contact with 

the surface was suggested by Higgins et al. [94] (Section 1.4). 

Within operational limits the AFM cantilever behaves as a linear, or 

‘Hookean’, spring. As a result the magnitude of the deflection of the cantilever 

can be used to calculate the force which is exerted on the cantilever 

using Hooke’s law: 

F � � kx 

(1.1) 

where F is force (N), x the deflection of the cantilever (m) and k the spring 

(or force) constant of the cantilever (N m �1 ), which essentially represents 

the stiffness of the cantilever. This spring constant is dependent upon the 

physical properties of the lever. This is apparent from the following relation, 

used to describe a rectangular, ‘diving board’ shaped lever as shown 

in 1. 5 [16, 95]: 

3 

Et w 

k � 3 

4l 

(1.2) 

where E is the Young’s modulus of the lever and t, w and l the thickness, 

width and length of the lever, respectively. However, it must be borne in 

mind that none of the diving board levers are perfectly rectangular, due 

to shaping of the ends of the beams and imperfections in the manufacturing 

process. As a result this equation will give only an approximate value 

for the stiffness of a rectangular cantilever. In the next section the need 

for the methods used to effectively measure the stiffness of a cantilever 

to be used for force measurements, whether it is rectangular or V-shaped, 

and the reasons for variability in k between cantilevers are addressed in 

greater detail. 

For different applications, cantilevers with different spring constants 

may be needed. For instance, for intermittent contact mode in air, particularly 

stiff levers are needed to overcome capillary forces, whereas for 

measurement of weak interaction forces, very soft levers are needed for 

their increased force sensitivity. The most convenient ways of producing 

this variation are by altering the length and or thickness of levers during 

production in order to increase or decrease the lever stiffness.


.6 CalIbraTIon of afm mICroCanTIlevers 

.6. Calibration of normal spring Constants 

For the accurate measurement of forces, the spring constant of the cantilever 

needs to be known. In particular, for forces normal to the surfaces 

of interest, this is the spring constant which governs the relationship 

between force and deflection in the z-direction, as opposed to the lateral 

and torsional spring constants (see Section 1.4.2). Although cantilevers 

are supplied with a manufacturers’ ‘nominal’ value, the actual value can 

vary to a high degree, mostly due to variations in the thickness of the 

levers and defects in the material of the cantilevers themselves. The cubic 

relationship between thickness and the spring constant seen in equation 

(1.2) means that small variations in thickness can cause significant variations 

in k. Because of this variability, for force experiments the cantilevers 

to be used need to be calibrated to determine a more accurate value of k. 

There are now a large number of methods by which the spring constant 

can be calculated, each with their own advantages and disadvantages. 

Four of the most extensively used approaches are described later. 

A number of methods exist which involve calculating spring constants 

based upon the dimensions and geometry of the lever. Whilst calculations 

for rectangular cantilevers, such as in equation (1.2), are relatively 

straightforward, for V-shaped cantilevers, approximations are most often 

used based upon a simplification of their geometry, e.g. Sader approximated 

a V-shaped cantilever to two parallel rectangular beams [96]. This 

resulted in the following equation to describe a V-shaped lever: 

3 

Et w ⎧ 3 

4w 

⎫ 

k � cos � 1 � 3 � 2 

3 ⎨ 

⎪ ( cos � ) 

3 

⎬ 

⎪ 

2l 

⎩ 

⎪ b 

⎭ 

⎪ 

�1 

(1.3) 

where � is the inside angle between the two arms of the V-shaped lever, 

w the width of each of the lever arms parallel to the base of the lever and 

b the outer width of the base of the lever (see Figure 1.5 for diagrammatic 

explanation of the dimensions). This equation, as well as equation 

(1.2), assumes that the point of loading of force on the cantilever will be 

at the very apex. As the probe tip itself, where the loading of force actually 

occurs, is often sited a short distance from the very end, this needs to 

be taken into account. A simple correction may be applied based on the 

length of the lever and the distance of the probe from the end of the lever 

[96–98]: 

k � k ( l/ ∆l) 3 (1.4) 

c m 

�

l 

1.6 CALIBRATION OF AFM MICROCANTILEvERs 7 

where k m is the uncorrected calculated spring constant value, k c the corrected 

value and �l the distance of the centre of the base of the probe 

from the apex of the lever. 

The problem with calculating spring constants purely from the measured 

dimensions of the lever and nominal values for the Young’s modulus is primarily 

that during cantilever manufacture variability in the material properties, 

particularly the Young’s modulus, of cantilevers can occur largely due 

to variations in the morphology of the silicon nitride [23]. In addition, accurate 

determination of lever thickness is not always very practicable. Making 

accurate measurements for every lever used in experiments by SEM is time 

consuming and not necessarily convenient. By measuring the resonance 

behaviour of cantilevers, variability in the material properties of the cantilevers 

can be at least to some extent taken into account. This leads to a more 

reliable calculation for the spring constant of a cantilever surrounded by a 

fluid environment, such as air, from the following relationship [99, 100]: 

2 2 

f i f f 

k � 0. 1906� 

b lQΓ 

( � ) � 

(1.5) 

where � f is the density of the surrounding fluid; Q the quality factor (a 

measure of the sharpness of the resonance peak); � i the imaginary component 

of the hydrodynamic function, dependent upon the Reynolds 

number of the fluid; and � f the fundamental resonance frequency of the 

cantilever. Although this approach is reliable for calibrating rectangular 

levers, there are not currently any reliable approximations to allow this 

method to be used for the commonly used V-shaped cantilevers. 

Another method, developed by Cleveland et al. [95], requires the 

attachment of known masses, such as tungsten spheres, to the end of the 

cantilever whilst monitoring the resultant resonant frequency change. 

Measuring the position of the fundamental resonance peak of the 

cantilever before and after the addition of the sphere allows the following 

relationship to be used to calculate the spring constant: 

2 M 

k � ( 2π 

) (1.6) 

( 1/ v ) � ( 1/ 

v ) 

1 2 

w 

0 2 

t 

fIgure .5 Diagram 

showing relevant dimensions 

on a beam-shaped 

AFM cantilever.


where M is the added mass, k the cantilever spring constant and v 0 and v 1 

the unloaded and loaded resonant frequencies. 

Although this method can produce a value for the cantilever 

spring constant to a high degree of accuracy, there are some problems. 

Attaching the bead to the cantilever, especially if attached using glue, 

can be a destructive process, rendering the lever unusable for further 

experiments. This means that calibration must be carried out at the end 

of experimental measurements. However, with sufficient care spheres 

may be attached in air using capillary adhesion forces alone. In addition 

errors may occur from the incorrect placement of the sphere or uncertainties 

in the mass of the sphere. If the sphere is placed a short distance 

away from the end of the lever, then the value obtained from this 

method will be high, as k is inversely proportional to the cube of the 

cantilever length l. Again, this can be simply accounted for by utilizing 

equation (1.4). 

The masses of spheres ordinarily used in this technique are on the 

order of a nanogram, making accurate weighing problematic. As such, 

masses are generally estimated from the size and density of the spheres, 

which may in turn lead to measurement errors. To allow for this, measurements 

may be made using several spheres of different masses. A plot of M 

versus (2�v 1) �2 can then be made, which will have a slope equal to the 

spring constant of the cantilever [95, 101]. The advantages of this method 

are that the measurements are independent of the cantilever geometry 

and material properties, and many commercially available AFMs have the 

capability to measure cantilever resonant frequencies. 

Another technique commonly used to quantify cantilever spring 

constants is the so-called ‘thermal method’ devised by Hutter and 

Bechhoefer [102, 103]. Here the area of the fundamental resonant peak 

of the cantilever under ambient thermal excitation, when not in the presence 

of a surface, can be used to directly calculate the spring constant of 

the cantilever. The mean square deflection of the cantilever, x 2 , due to 

thermal fluctuations can be related to the spring constant thus, assuming 

an idealised spring behaviour: 

kBT k � 

2 

x 

(1.7) 

where k B and T are Boltzmann’s constant (1.38 � 10 �23 J K �1 ) and absolute 

temperature, respectively, together representing the thermal energy 

of the system. Once other noise sources are subtracted from the background, 

the area of the fundamental resonance peak will be equal to the 

mean square displacement. However, as the cantilever is not an ideal

spring, equation (1.7) is insufficient to describe its behaviour, and a number 

of other factors may need to be taken into account [103–107]: 

2 

0. 8174s kBT 1 � 3Dtan / 2l 

k � 

P 1 � 2Dtan 

/ l 

cos 

⎛ ϕ ⎞ 

⎜ 

ϕ 

⎝⎜ 

ϕ ⎠⎟ 

(1.8) 

where D is the tip height, s the sensitivity (in V or A m �1 ), and P the positional 

noise power of the fundamental resonance peak (the area under 

the fundamental resonance peak in the power spectral density (PSD) 

curve), obtained from a plot of the thermal power spectrum. Thus, with 

a spectrum analyser and appropriate software available with a number 

of commercially available AFM instruments, spring constant calibration is 

relatively straightforward as well as being relatively non-destructive. 

Higgins et al. [94] suggested a novel way of finding the optical lever 

sensitivity by combining this thermal method with those of Sader. By 

using Sader’s method to determine a spring constant for the cantilever, 

the method of Hutter and Bechhoefer could then be used to back- 

calculate the optical lever sensitivity without the need to make a hard contact 

with a stiff surface. This method is potentially of use where a hard 

contact is undesirable, for instance when the probe is chemically functionalised 

or when a particle made of some deformable material, which is likely 

to significantly deform under measurement stresses, is used as a probe. 

A very simple and straightforward method of calibrating the cantilever 

spring constant is to press the cantilever to be calibrated against another, 

reference, cantilever of known k (Figure 1.6). This could be either a macroscopic 

lever [108] or another AFM microcantilever [109]. Reference 

cantilevers can be obtained either commercially or by using another calibration 

method or combination of other methods to determine k to a high 

precision. When the two levers are pressed together, the slope of the contact 

region on the force curve will be the result of the deflection of both 

levers. As a result, comparison of this slope with the slope obtained when 

b 

w 

1.6 CALIBRATION OF AFM MICROCANTILEvERs 

w ′ 

t 

α 

l ′ 

l 

2 

fIgure .6 Diagrammatic 

representation of a 

V-shaped AFM cantilever.


pressed against a hard surface, which will not appreciably deform under 

the pressure exerted upon it, will allow the calculation of the unknown 

spring constant, providing that the same optical lever set-up and hence 

its sensitivity remains unchanged between each set of measurements: 

k � k 

c ref 

⎛ �hard � � ⎞ 

⎜ 

ref 

⎜ 

⎝⎜ 

�ref � cosϕ 

⎠⎟ 

⎛ 

� 

⎞ 

⎜ hard 

kc � k ⎜ ref ⎜ � 1 

⎝⎜ 

�ref 

⎠⎟ 

(1.9) 

(1.10) 

where k c and k ref are the spring constants of the unknown and known 

reference levers, � hard and � ref the gradients of the contact regions of force 

curves against a hard surface and the reference lever, respectively, ϕ the 

angle between the two levers. 

Typically levers are mounted onto the AFM with an in-built tilt angle of 

approximately 10–12°, which is liable to give a value of k varying from the 

true value by less than the experimental uncertainty. In addition, if care is 

taken to maintain the same angle between the lever and the experimental 

sample when calibrating the lever, then the apparent spring constant calculated 

by this method will be identical to the effective spring constant. As such 

the term cos ϕ can be ignored (equation (1.10)). This is a quick and simple 

method to use and can be carried out where the instrumentation being used 

does not allow the measurement of the resonance spectrum of the cantilever. 

One area where caution must be taken with the reference lever method 

is in the precise positioning of the two levers (Figure 1.7). As seen from 

equation (1.2), k will vary inversely in relation to l 3 . This means that if the 

cantilever to be calibrated overlaps with the reference lever, effectively 

reducing the length of the reference, the measurements obtained will be 

as though taken against a stiffer reference lever, leading to an underestimation 

of k c. Another important factor to consider is that the stiffness of 

the unknown cantilever and the reference must be similar in order to get 

a truly accurate result. If one cantilever is much stiffer than the other, then 

the slope obtained from a force curve of the cantilevers pressed together 

k ref 

k c 

ϕ 

fIgure .7 Static def- 

lection of a cantilever of 

unknown spring constant 

against a reference cantilever. 

The slope of the contact 

region of the resultant 

force curve is dependent 

upon the stiffness of the two 

levers combined as well as 

the angle between them.

will be dominated by the deflection of the softer lever. It has been suggested 

that one lever should not have a spring constant greater than the 

other by more than a factor of three [109] for this method to be effective. 

This is only a selection of some of the more commonly used techniques. 

There are a large number of other methods used to determine 

spring constants of AFM cantilevers listed in the literature. These include, 

in no especial order, the measurement of the dynamic response of cantilevers 

with colloidal spheres attached in a viscous fluid [110, 111]; calculating 

k of levers on a chip, based on geometry, compared with a lever on 

the same chip calibrated by another method [97]; an alternative ‘thermal 

method’ with k calculated from the resonant frequency, Q factor and the 

squared resonance amplitude [112]; and measuring the static deflection 

of an AFM cantilever due to a known end-loaded mass [113]. 

.6.2 Calibration of Torsional and lateral spring Constants 

To extract quantitative data from measurements of lateral forces experienced 

by the probe when scanning across a surface, such as in friction 

force microscopy, then the stiffness of the cantilever in the lateral or torsional 

mode needs to be ascertained. However, this is much less straightforward 

than calibrating the normal spring constant of the lever. For 

frictional measurements, as well as knowledge of the normal and torsional 

spring constants, knowledge of the lateral response of the deflection 

sensor and the geometry, height and material properties of the probe 

at the region of contact with the sample need to be ascertained. 

At this point the difference between the torsional and lateral stiffnesses 

of the cantilevers must be made clear. The torsional spring constant k � is the 

resistance to rotation along the major axis of the cantilever. The lateral spring 

constant k lat on the contrary is the resistance of the lever to forces experienced 

laterally at the apex of the probe tip, producing a rotation at the base 

of the probe. The two are related by the following simple formula [114]: 

kΦ 

klat 

� 2 

h 

(1.11) 

where h is the height of the probe (usually in the region of 3 μm for most 

imaging probes). 

Sader described equations to calculate the approximate k� for both 

beam-shaped and V-shaped cantilevers [115] from their geometries. 

Torsional stiffness for a beam-shaped cantilever is: 

k 

φ 

1.6 CALIBRATION OF AFM MICROCANTILEvERs 2 

⎧⎪ 

⎛l 

� l 

3 

tanh ⎜ 

∆ ⎞ ⎫ 

⎪ 

⎪ 

� v 

Et w ⎪ 

6( 1 ) ⎪ 

⎝⎜ 

w 

⎠⎟ 

w ⎪ 

� ⎨ 

⎪1 

� 

⎬ 

⎪ 

6( 1 + v)( l − ∆l) 

⎪ 

6( 1 � v) 

l � ∆l⎪ 

⎪ 

⎪ 

⎩⎪ 

⎭⎪ 

�1 

(1.12)


and for torsional forces experienced by a V-shaped cantilever: 

k 

φ � 

3 

2 

Et w w ⎛2w 

l ⎞ 3⎛ 

b⎞ 

1 

1 � 2log⎜ 

� 2 � ⎜ 

3( 1 � v) l b ⎝⎜ 

b ∆l⎠⎟ 

8 ⎝⎜ 

l ⎠⎟ 

1 �� b 

⎧⎪ 

⎡ 

2 

⎛ ⎞ ⎤⎫ 

⎪ 

⎪ 

⎪ ⎢ 

⎜ 

⎥⎪ 

⎪ ⎢ 

⎜ 

⎥ 

⎪ 

⎨ 

⎪ ⎢ 

⎜ 

⎢ 

⎜ 

⎥ 

⎜ 2 

⎢ 

⎜ 

⎥ 

⎬ 

⎪ 

⎪ 

⎪ 

⎪ 

2 

⎢ 

⎝⎜ 

4l 

⎠⎟ 

⎥⎪ 

⎪ 

⎥ 

⎪ 

⎩⎪ 

⎣ 

⎦⎭⎪ 

−1 

(1.13) 

where �l is the distance of the base of the probe tip from the apex of the 

lever. 

For relevant dimensions of the levers see Figures 1.5 and 1.6. In terms 

of measured interactions, k lat can be defined in similar terms to Hooke’s 

law for the normal spring constant of the lever [73]: 

Flat � klat∆ x 

(1.14) 

where F lat is the force experienced by the tip and �x the lateral movement 

of the tip along the x-direction (i.e. at right angles to the major axis 

of the cantilever). 

.7 ColloId probes 

By attaching a microsphere to the end of a tipless cantilever, the geometry 

of interactions between the probe and the surface can be greatly simplified, 

allowing the AFM to be used to probe surface forces, much akin to the 

surface force apparatus (SFA). Microparticles can also be used as probes, 

which will allow particle to particle adhesion forces to be measured. 

An example of a colloid probe is illustrated in Figure 1.8. Here a scanning 

fIgure .8 SEM image 

of a colloid probe created 

by the attachment of a silicon 

dioxide sphere to the 

apex of an AFM microcantilever 

using an epoxy 

resin. The scale bar shown 

is 1 �m long, with the particle 

approximately 5 �m in 

diameter.

ABBREvIATIONs ANd syMBOLs 23 

electron microscope (SEM) image shows a 5-μm diameter silica bead 

attached with glue close to the apex of a standard AFM microcantilever. 

The first reported use of an AFM with a colloidal probe was by Ducker 

et al. [116, 117] who attached a 3.5-μm silica sphere to an AFM cantilever 

and used it to measure forces between the sphere and a silica surface as 

a function of electrolyte concentration and pH. Since then this technique 

has been used to probe the interaction forces between various materials 

and surfaces including silicates and other inorganic materials [80, 83, 117, 

118], protein- and polymer-coated beads and surfaces [119–122], membrane-fouling 

materials and membranes [123], biological cells and surfaces 

[124, 125]; between drug particles which are important in powder 

formulations [81, 84, 87]; and for probing the rheological properties of 

liquids [110, 126]. See Chapter 2 for more detail on the preparation of colloid 

probes. 

abbrevIaTIons and symbols 

AFM Atomic force microscopy/microscope 

b Outer width of the base of V-shaped cantilever m 

E Young’s modulus N m�2 F Force normal to sample surface N 

Flat Lateral forces N 

JKR Johnson, Kendall and Roberts theory 

k Spring constant of cantilever N m�1 kB Boltzmann’s constant (1.38 � 10�23 ) J K�1 kc Corrected k N m�1 klat Lateral spring constant N m�1 km Uncorrected k N m�1 kref Reference cantilever spring constant N m�1 k � Torsional spring constant N m �1 

l Cantilever length m 

M Mass added to cantilever kg 

P Positional noise power of fundamental resonant peak 

PDMS Polydimethylsiloxane 

Q Quality factor of cantilever – 

SPM Scanning probe microscopy 

STM Scanning tunnelling microscopy/microscope 

t Cantilever thickness m


T Absolute temperature K 

v 0 Unloaded resonant frequency Hz 

v 1 Loaded resonant frequency Hz 

w Cantilever width m 

x Deflection of cantilever m 

� Inside angle of V-shaped cantilever ° 

� i Imaginary component of hydrodynamic function – 

� hard Contact slope versus hard surface nm V �1 

� ref Contact slope measured versus reference cantilever nm V �1 

� f Density of surrounding fluid Pa s 

ϕ Angle between cantilever and reference lever ° 

� f Fundamental resonant frequency of lever Hz 

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C H A P T E R 

2 

Measurement of Particle 

and Surface Interactions 

Using Force Microscopy 

Nidal Hilal, Daniel Johnson, W. Richard 

Bowen and Paul M. Williams 

O U T L I N E 

2.1 Introduction 32 

2.2 Colloid Probes 32 

2.3 Interaction Forces 35 

2.3.1 van der Waals Forces 35 

2.3.2 Electrical Double Layer Forces 44 

2.3.3 DLVO Theory 53 

2.3.4 Solvation Forces 58 

2.3.5 Steric Interaction Forces 62 

2.3.6 Hydrophobic Interaction Forces 63 

2.3.7 Effect of Hydrodynamic Drag on AFM Force Measurements 66 

2.4 Adhesion Forces Measured by AFM 67 

2.4.1 Contact Mechanics and Adhesion 67 

2.5 Effect of Roughness on Measured Adhesion and Surface Forces 70 

Abbreviations and Symbols 70 

Greek Symbols 73 

References 74 

Atomic Force Microscopy in Process Engineering 31 

© 2009, Elsevier Ltd

32 2. MEASUREMENT OF PARTICLE ANd SURFACE INTERACTIONS 

2.1 IntRoduCtIon 

In Chapter 1, discussion was made of the application of the AFM to 

the measurement of forces. In this chapter, we will describe the use of the 

AFM to quantitatively measure surface forces arising from the interactions 

between particles and between particles and surfaces. These forces 

are of particular interest in the study of colloidal dispersions, where the 

strength of interactions between particles governs the properties of the 

dispersion overall. 

Most traditional methods used to study colloidal dispersions are 

ensemble techniques, where the interactions of a large number of particles 

are measured simultaneously. The advantage with the AFM is the ability 

to make measurements on the single-particle level and to measure forces, 

and hence interaction energies, with respect to intersurface distances. 

Depending upon the experimental set-up being employed, a number of 

different interactions may be measured, either separately or simultaneously, 

including long-range forces such as van der Waals and electrical 

double layer forces, hydrophobic interactions, solvation forces, steric 

interactions, hydrodynamic drag forces as well as adhesion. In this chapter, 

the forces that are likely to be encountered when measuring interactions 

between particles and between particles and surfaces whilst using 

the AFM are described, with examples of the measurements extant in the 

literature being included. It is hoped that this chapter will serve as a useful 

and practical guide to anyone who is undertaking such measurements. 

2.2 ColloId PRobES 

By replacing the pyramidal or conical probe usually present on an 

AFM cantilever with a microsphere, the geometry of interactions between 

the probe and surface can be greatly simplified, allowing the AFM to be 

used to probe surface forces, much akin to the surface force apparatus 

(SFA). Microparticles can also be used as probes, which will allow 

particle-to-particle adhesion forces to be measured. An example of a colloid 

probe is shown in Figure 2.1. Here, a scanning electron microscope (SEM) 

image shows a 5 �m diameter silica bead attached with glue close to the 

apex of a standard AFM microcantilever. 

As the size of a spherical colloid probe is increased, the potential area 

of contact will also increase in proportion. For two spheres in close proximity, 

the force as a function of distance D is: 

R R 

F( D) 

W( D) 

R R � 

1 2 

2π 

� 

⎛ ⎞ 

⎜ 

⎝⎜ 

⎠⎟⎟ 

1 2 

(2.1)

2.2 COLLOId PROBES 33 

FIGuRE 2.1 SEM image of a colloid probe created by the attachment of a glass sphere 

to the apex of an AFM microcantilever using an epoxy resin. The scale bar shown is 5 �m 

long, with the particle approximately 7.5 �m in diameter. 

where R 1 and R 2 are the radii of the two spheres and W(D) is the interaction 

energy per unit area as a function of distance [1, 2]. This relationship 

is referred to as the Derjaguin approximation. In the case of a sphere 

approaching a flat surface (or where one sphere is much greater in size than 

the other), this is further simplified to create: 

F( D) � 2πR1W( D) 

(2.2) 

Note that the forces of interaction are proportional to the radius or radii 

of the interacting spheres. For this reason, it is typical in colloidal probe 

measurements to normalise forces by dividing by the radius of curvature 

of the probe. This generally leads to forces being measured in units of the 

form of mN m �1 . It should be noted that one of the assumptions on which 

the Derjaguin approximation is based is that the range of the interaction 

forces is much less than the radii of the interacting spheres. For small 

spheres with radii in the nanometre range, this approximation is likely 

to be invalid, a situation that has been recently experimentally verified 

by carrying out measurements using AFM tips terminated with particles 

with radii of 10 and 20 nm [3]. Dividing the forces by the particle radii was 

insufficient to superimpose the force traces obtained with these particles. 

Colloidal probes are most commonly prepared by attaching the particle 

to the apex of the AFM cantilever with an appropriate glue using a


micromanipulator set-up, although where materials allow, sintering may be 

used, such as with polystyrene beads. Figure 2.2 shows a typical micromanipulator 

set-up, utilised in the preparation of colloid probes. This consists 

of a micromanipulator platform positioned underneath an optical microscope, 

and connected to an electronic control unit. Colloidal particles are 

placed upside down on a cleaned microscope slide, where they adhere via 

capillary forces. At one end of the slide is placed a thin smear of an appropriate 

adhesive. The AFM cantilever is allowed to come into contact with 

the glue, with care being taken to minimise the amount of glue present. Too 

much glue may cause problems with contamination. Any excess can be 

wiped off by scraping the cantilever carefully on a clean area of the slide. 

The stage is then moved until a suitable particle is located. The cantilever 

plus glue is then allowed to come into contact with the particle, removing it 

from the surface of the slide. The glue is allowed to set and the probe is then 

ready for use. An alternative method also used is to place a drop of glue on 

the end of the cantilever using a fine wire. Another wire is then used to pick 

up a particle using capillary adhesion and then place it on the glued end of 

the lever [4]. 

C 

A 

D 

FIGuRE 2.2 Illustration of a typical micromanipulator set-up. It consists of a movable 

stage (A) mounted below an optical microscope (B). Inset into the top-left corner is a closeup 

of the stage. Movement of the stage can be controlled via an electronic control console 

(C), shown here on the left. Cantilever, particle interaction can also be monitored via a digital 

video camera (D) mounted on the microscope. The AFM cantilever is introduced to the 

underneath of a microscope slide mounted on the stage from the left, where it is allowed to 

come into contact with glue and particles attached to the slide. Fine control of the cantilever’s 

movement is attained via the manipulator joystick and vertical drive (E). On the monitor, 

a V-shaped AFM cantilever is visible. The picture was taken in the laboratory of the 

Department of Chemical and Environmental Engineering, University of Nottingham. 

A 

B 

E

2.3.1 van der Waals Forces 

2.3 IntERACtIon FoRCES 

In the nineteenth century, J. D. van der Waals derived an equation of 

state to account for deviations in the observed behaviour of gases from 

the ideal gas law, pV � nRT: 

⎛ 2 

n a ⎞ 

⎜ VW ⎜ 

⎜p 

� ( V � nbVW ) � nRT 

2 

⎝⎜ 

V ⎠⎟ 

(2.3) 

where p is the pressure, V is the volume of the container, n is the number 

of gas molecules in moles, R is the gas constant and T is the temperature. 

This equation contained two new terms to account for deviations from 

ideal behaviour, which can be determined experimentally and which vary 

between different types of molecule; a vw, which accounts for attractive 

forces between the molecules and b vw, which accounts for the volume of 

space occupied by the gas molecules and from which other molecules are 

excluded. This exclusion leads to repulsive forces at short ranges, due to the 

Pauli exclusion principle. Whilst there is a wide range of interactions that 

may occur between atoms, molecules and materials made from them, the 

term ‘van der Waals forces’ has been applied to a set of attractive forces that 

have their origin in interactions between dipoles, both permanent and temporarily 

induced, present in atoms and molecules. They can be divided 

into three types depending upon the precise nature of the interaction: 

dipole-dipole interactions (Keesom forces); dipole-induced dipole interactions 

(Debye forces) and interactions between dipoles induced on opposing 

atoms or molecules (London or dispersive forces), and thus all are of an 

electrostatic origin. The Keesom and Debye forces act between polar molecules. 

However, the London dispersive forces may arise between neutral 

atoms and are thus potentially present in all interactions between materials. 

All of these forces have interaction potentials of the form: 

w 

( r) 

2.3 INTERACTION FORCES 35 

CT 

( CK � CD � CL 

) 

� � � 

6 6 

r 

r 

(2.4) 

where w (r) is the interaction potential, C t is the constant of the interaction 

and r is the closest separation distance between molecules – subscripts 

K, D and L denote Keesom, Debye and London interactions respectively. 

When reading the literature, it is important to bear in mind which forces 

are being referred to by the term van der Waals forces. Some authors 

include all three of the types of dipole interactions mentioned here as 

van der Waals forces, whilst other authors specifically only mean the 

dispersion component of the interaction.


All van der Waals interactions decrease to the inverse sixth power 

of the separation distance. In effect, this means that these forces are not 

significant at ranges greater than the order of 100 nm and are unable 

to produce alignment effects in liquids at long ranges [2]. One simple 

approximation of the combined attractive van der Waals forces combined 

with the short-range electron shell repulsion is the Lennard-Jones 

potential [2, 5]: 

w 

( r) 

A B 

� � � � � 

r r r r 

4 

12 6 

� � 

� ⎛ ⎡ ⎞ ⎛ ⎞ ⎤ 

⎢⎜ 

⎜ ⎥ 

⎢⎝⎜ 

⎠⎟ 

⎝⎜ 

⎠⎟ 

⎥ 

⎣⎢ 

⎦⎥ 

6 12 

(2.5) 

where � is the depth of the potential energy well, � is the distance at 

which the potential energy is zero. In the simpler form on the right, 

A � 4�� 6 and B � 4�� 12 , which are the attractive and repulsive components 

of the Lennard-Jones potential respectively. Whilst the attractive 

component declines to the sixth power, the repulsive short-range forces 

decline to the twelfth power. This leads to a change in interaction potential 

with distance, as illustrated in Figure 2.3. At large distances, interaction 

forces are insignificant. On close approach between the molecules, attractive 

(negative sign) forces begin to dominate, with the potential reaching 

a minimum before repulsive forces from repulsion of opposing electron 

shells dominate. 

Keesom or orientational forces arise from the angle averaged interactions 

between permanent dipoles on opposing molecules. This gives rise 

to the following interaction free energy w (r): 

w 

( r) 

u u 

CK 

u1u2 � � � � for kT � 

2 6 6 

3( 4πε ε ) kTr r 

4πε 

ε r 

0 

1 2 2 2 

r 

0 

r 

3 

(2.6) 

where u 1 and u 2 are the dipole moments of the two molecules or atoms, 

ε 0 is the permittivity of free space (8.854 � 10 �12 C 2 J �1 m �1 ), ε r is the 

dielectric constant of the intervening medium, k is the Boltzmann constant 

(1.380 � 10 �23 J K �1 ) and T is the absolute temperature. The interaction 

between the dipoles increases the probability of an orientation 

between the dipoles, which leads to mutual attraction. 

The Debye, or induction, interaction is a result of permanent dipoles 

inducing temporary dipoles in opposing molecules and is the angle averaged 

interaction between such dipoles. The resulting free energy from 

such an interaction is: 

w 

( r) 

[ u 02 � u2 

] C 

� � 

� � 

( ) r r 

2 α �01 

4πε 

ε 

1 2 

0 

r 

2 6 

D 

6 

(2.7)

Interaction potential, w(r) 

0 

where � 01 and � 02 are the electronic polarisabilities of the two molecules. 

Both the Keesom and the Debye interactions involve polar molecules 

and are thus not always present, depending upon the molecules involved 

in the interaction. However, the dispersive, or London, component of 

the interaction described by London during the 1930s is always present. 

As two molecules come into close proximity, the repulsion between 

the negative charges in the electron shells causes the induction of temporary 

dipoles. As the molecules do not have to be polar and can be 

electrically neutral, this interaction can and does occur between any molecules 

within sufficient range of each other. The interaction free energy 

for the dispersion interaction between two molecules can be described as 

follows [6, 7]: 

w 

( r) 


3 �01�02 hv1v2 C 

� � 

� � 

2 6 2 ( 4πε 

) r ( v � v ) r 

0 

1 2 

w (r) 

Attractive 

Repulsive 

0.2 0.4 0.6 0.8 1 

Distance (nm) 

FIGuRE 2.3 Sketch of the Lennard-Jones potential for an interacting molecular pair 

described by equation (2.5). Also shown are the individual attractive and repulsive components. 

As the two molecules approach, attractive forces increase until repulsive forces due 

to the proximity of the electron shells of the molecules overcome the attraction. 

L 

6 

(2.8) 

where v 1 and v 2 are the orbiting frequencies of electrons, and h is Planck’s 

constant (6.626 � 10 � 34 m 2 kg s �1 ).


2.3.1.1 van der Waals Forces Between Bulk Materials 

For the useful estimation or measurement of van der Waals interaction 

forces between colloidal particles and/or surfaces, the theory outlined 

in the previous section needs to be extrapolated to describe the behaviour 

between materials rather than purely between individual atoms or 

molecules. A molecule at the surface of a particle in close proximity to 

another will interact with its neighbouring molecules, with molecules 

on the opposing particle as well as with the constituent molecules of the 

intervening medium. The summation of all the pair potentials interacting 

between macroscopic bodies results in forces that decay much more 

slowly with distance than is the case for single molecular interactions [2]. 

The effect of the dispersion force was investigated theoretically by 

Hamaker [8] and de Boer [9]. For interactions between spherical particles, 

they used a pairwise summation of the interatomic dispersion energies and 

demonstrated that although the range of the atomic forces was of the range 

of atomic dimensions, the sum of all of the dispersion energies resulted in 

an interaction range for colloidal bodies of the order of their dimensions. 

In other words, when scaled up to particles containing a great number of 

atoms, the range of the forces no longer decreases by the sixth power of 

the distance when separation is small compared to the size of the particles 

[10]. The coefficient of interaction used by Hamaker is now referred to as 

the Hamaker constant (A H). However, pairwise additivity does not hold 

especially if the interaction is occurring in a condensed medium, such as 

a liquid. This is because nearby atoms affect the forces acting between any 

interacting pair of molecules within a close vicinity [2]. 

Lifshitz later described a macroscopic approach that completely 

avoided the problems associated with additivity, neglecting atomic structure, 

treating large bodies as continuous media with forces being derived 

in terms of bulk properties such as the dielectric constants and refractive 

indices [11]. In Table 2.1, the interaction energies and forces are listed for 

geometries of spherical particles interacting with other spheres and flat 

planes in terms of the Hamaker constant, A H, minimum separation distance 

and sphere radii. Here, the force is the negative differential of the 

potential with respect to the minimum separation: 

F 

dVA 

� � 

dD 

(2.9) 

The Hamaker constant contains elements describing all the material 

properties of the systems of interest. It can be summarised by the following 

formula: 

A � π C� 

� 

H 

2 

1 2 

(2.10)

TABLE 2.1 Energy and force expressions for different geometries. 

Two spheres 

R 1 

D 

Identical spheres 

R 

D 

Sphere – Plane 

R 

D 

Paraboloid – Plane 

R 2 

R 


V 

V 

V 

V 

A 

A 

A 

A 

AH 

= 

R R 

D R R 

− 

1 2 

6 + 

A R H 

= 

D 

− 

12 

A R H 

= 

D 

− 

6 

A 

= 

l 

D l 

− 

12 

1 2 

A R R 

H 

F = 

D R R 

− 

6 + 

2 

1 2 

A R H 

F = 

D 

− 

12 2 

A R H 

F = 

D 

− 

6 2 

1 2 

where � 1 and � 2 are the number of atoms per unit volume in the two 

interacting materials. 

There are some general properties of van der Waals interactions 

between macroscopic bodies, which are worthy of note. First, interactions 

between two bodies across vacuum are always attractive, as are all interactions 

between two bodies of identical composition across a medium. 

However, for two bodies of dissimilar materials, the net interaction may 

be either attractive or repulsive, depending upon the particular setup. 

Whilst all van der Waals interactions per se are attractive, if one of 

the bodies has a greater attraction for the intervening medium than for 

the opposing body, then this will result in a net repulsion between the 

two bodies [12]. Whether such an interaction is likely to be attractive or 

repulsive can be assessed by comparison of the dielectric constants of the 

materials involved. If the dielectric constant of the intervening medium 

is between that of the materials of the two bodies, then the net forces 

between the two bodies will be repulsive. If it matches the dielectric constant 

of either of the interacting bodies, then the van der Waals force will 

effectively vanish [13]. 

H xy 

2 

2 

z 

2 

xy 

2 

z 

A j 

H 

F = 

D l 

− 

12 2


2.3.1.2 Retardation of van der Waals Forces 

As the distance between interacting atoms increases, the time for the 

electric field of one atom to interact increases, and for a large enough distance 

will become comparable with the time over which the dipole itself 

fluctuates, leading to fluctuations in the interacting dipoles becoming out 

of step. This can lead to the interaction becoming less favourable, causing 

the strength of the interaction to decrease with the inverse seventh 

power of the separation distance rather than to the inverse sixth power 

[2, 14]. Because of this mechanism, it is only the London dispersion interactions 

that are affected by these retardation affects and not the Debye or 

Keesom interactions. 

2.3.1.3 Calculation of Hamaker Constants 

Looking at Table 2.1, it can be seen that if the Hamaker constant is 

known, it is possible to calculate the interaction energy between surfaces, 

provided that particle radii and distances of separation are available. The 

Hamaker constant though is not an easily obtained value. 

Lifshitz theory [11] can be used to calculate the Hamaker constant, 

but the calculations require complete knowledge of the dielectric spectra 

over the entire frequency range for all of the individual materials comprising 

the system. This type of data is not available for most substances, 

so another method is required for which data is more widely available. 

Ninham and Parsegian [15] considered the construction of the dielectric 

spectra for all frequencies and concluded that not all parts of the 

frequency range are equally important. They found that the ultraviolet 

absorption regime is the most important of all the contributions to the 

frequency sum. Hough and White [16] also emphasised the importance 

of the ultraviolet absorption peak. To obtain the parameters for the UV 

peak, refractive index data measured over a range of wavelengths, �, 

usually in the visible part of the spectrum, can be used. The following 

equation was then constructed [16]: 

2 2 ω 

no ( ω) � 1 � ( no ( ω) 

� 1) 

� C 

2 

ω 

2 

UV 

UV 

(2.11) 

π 

where ω� 

λ 

2 c , no(�) is the refractive index at a given frequency and c is 

the speed of light in a vacuum. 

2 

2 

Thus, if a graph of ( no � 1) 

is plotted versus ( no �1) �2 , a straight line 

2 

of slope 1/ωUV 

and intercept CUV will be obtained. This method of analysis 

is called the ‘Cauchy Plot’.


Horn and Israelachvili [17] presented an expression for the Hamaker 

constant, which is as follows: 

AH � A � Aξ � A 

o ξ� 

131 1 

(2.12) 

where the two terms in this equation may be found using the Cauchy 

Plot data from: 

where 

A 

ξ 

�1 

3 

⎛εr 

( 0) �ε 

r ( 0) 

⎞ 

⎜ 1 2 

Aξ�kT⎜ o 4 

⎜ 

⎝⎜ 

εr 

( 0) �εr 

( 0) 

⎠⎟ 

n 

o 

2 2 

o o 

n n 

� 

� 

2 

1 3 

2 2 

o o o 

∆n �n �n 

1 3 

ω1 

2 ω3 

2 

X � ( n o �1) � ( n o �1) 

1 3 

ω 

ω 

3 

1 2 

2 2 

o o o o 

3ℏ 

ωω 1 3 Xn�2XΔnn�Δn ( 3�2Y) � 

7/ 4 

64no 

⎡ 

1/ 2 

/ ⎤ 

⎢ 2 

2 

( Y � Y �1) 

� ( Y � Y � 1) 

⎥ 

⎣ 

⎢ 

⎦ 

⎥ 

1 ⎡ ω1 

2 ω ⎤ 

Y � ⎢ 

3 2 

( n o �1) � ( n o �1) 

⎥ 

1 3 

4 n ⎢ 

o ⎣ω 

3 ω ⎥ 

1 ⎦ 

1 

(2.15) 

(2.16) 

(2.17) 

(2.18) 

and ε ( 0) ri is the dielectric constant of component i, � is Planck’s constant 

divided by 2�, k is Boltzmann’s constant, n is the refractive index of com- 

oi 

ponent i (calculated from C UV �n o � 

2 

1), T is the absolute temperature, 

�i is the ultraviolet characteristic adsorption frequency of component 

i (i.e. � �UVi), subscript 1 refers to the material and subscript 3 to the dispersion 

medium. 

Therefore, if the dielectric constant and refractive index versus wavelength 

data are known for each component, i, the Hamaker constant may 

be approximated by use of a Cauchy Plot and the above equations. 

2 

1 2 3 

(2.13) 

(2.14)


Equation (2.12) is the expression for the non-retarded Hamaker constant. 

When comparing Hamaker constant data with literature values, 

this equation should be used, as the values given in the literature are for 

non-retarded Hamaker constants. However, in calculations where particles 

in an electrolyte solution are considered, and for some cases at large 

interparticle separations, the effects of retardation [18] and screening [19] 

on the Hamaker constant calculation need to be taken into account. This 

can be done by modifying equation (2.12) to: 

where 

A 131 �A ( 1�2κD) e + 

A F( H) 

ξ 

o 

�2κD 

F H 

H 

⎡ 

( ) � ⎢ ⎛ π ⎞ 

1�⎜ 

⎢ ⎝⎜ 

4 2 ⎠⎟ 

⎣⎢ 

3/ 2 

�2/ 

3 

D 

H �no ( n o �n 

3 1 o ) 

3 c 

/ w w 

⎤ 

⎥ 

⎦⎥ 

2 2 1 2 1 3 

(2.19) 

(2.20) 

(2.21) 

2.3.1.4 Calculation of van der Waals Forces from 

Force Distance Curves 

Measurement of the van der Waals interactions between different 

materials in different media is possible using the AFM. By changing 

the sharp probe with a colloidal particle, a wide range of different 

interactions can be measured. However, much care must be taken with 

the design of experiments. In many situations, forces other than van 

der Waals interactions may be present, such as double layer interactions 

and hydrodynamic effects, which may make it difficult or impossible 

to extract accurate estimations of van der Waals forces or Hamaker 

constants. In addition, any calculations made must take into account the 

probe sample interaction geometry. In the case of a spherical particle versus 

a plane surface or other spherical particles, this is relatively straightforward. 

However, for an irregularly shaped particle or one exhibiting 

significant surface roughness, then this is not a straightforward matter. 

This subject is dealt with in more detail in Section 2.5 of this chapter. 

There are several ways in which Hamaker constants may be estimated 

from AFM force measurements. First, one of the power laws, appropriate 

for the interaction geometry used in the experiment, from Table 2.1 may 

be fitted to the part of the force distance measurement obtained when 

the probe is approaching the surface just prior to any jump-to-contact. 

During the jump-to-contact event, the cantilever system is out of equilibrium 

and consequently, the power laws may not be fitted to this part 

ξ 

�1

of the force curve. Researchers have overcome this problem by the use 

of magnetically actuated cantilevers operating under a feedback mechanism 

to maintain the stability of the system [20]. 

Butt et al., in a comprehensive review of force measurement techniques 

[21], describe a method for calculating the Hamaker constant from both the 

jump-in distance and the deflection of the cantilever due to the jump-in. This 

requires knowledge of the radius of curvature of the probe tip (or spherical 

particle replacing the probe) along with the effective stiffness of both the 

cantilever and total system. For a sphere approaching a plane surface, 

A 

H 


3 

jtc 

3 

kc 

⎟ keff 

2 

3k D ⎛ 

eff jtc 2k ⎞ 

⎜ 3k x 

C eff 24 

� � ⎜ � 

Rt 

⎝⎜ 

keff 

⎠ Rt 

Rt 

(2.22) 

where D jtc is the jump-in distance, x jtc is the cantilever deflection due to 

the jump-in, R t is the radius of curvature of the probe tip, k c is the spring 

constant of the cantilever and k eff is the effective spring constant of the 

cantilever-sample system. The effective stiffness can be calculated from 

considering the contribution to the stiffness of the system of the cantilever 

and sample surface interacting in series: 

1 1 1 

� � 

keff kc ks 

(2.23) 

where k s is the stiffness of the sample, assuming negligible deformation 

of the probe. For hard samples or soft cantilevers, k eff � k c. Das and colleagues 

[22] used a similar approach to measure the Hamaker constant 

between silicon nitride AFM probes and a number of surfaces from the 

jump-in distance using the following relationship: 

A 

H 

k D 

� 

R 

24⎛ 

⎜ 

27⎝⎜ 

c jtc 

t 

⎞ 

⎠⎟ 

(2.24) 

Measurements were carried out on a SiO 2 surface, freshly cleaved 

mica and on a silver metal film in air under ambient conditions. Values 

obtained were of the same magnitude, but not identical, to literature values 

obtained from Lifshitz theory and measurements with the surface 

forces apparatus (SFA). One possible reason for this divergence may be 

the presence of a contaminating water layer present on most surfaces 

under ambient conditions. 

The Hamaker constant for an interaction may also be calculated from the 

work of adhesion, W a, between the two bodies. The work of adhesion may 

be obtained from the adhesion as measured during the retract cycle of a force 

distance measurement and then applying the appropriate contact mechanics


model. These models will be described in more detail later in this chapter. 

The particular relationship between W a and A H depends again upon the particular 

geometry of the interaction. For a sphere–plane interaction [21], 

AH � 6D0 Wa 

(2.25) 

This is essentially the same as the force laws found in Table 2.1, replacing 

the minimum separation distance, D, with an interatomic spacing 

value. In turn, W a may be related to the interfacial energies by the following 

relationship: 

Wa � � � � � � 

13 23 12 

(2.26) 

where � is the interfacial energy, subscripts 1 and 2 denote the two solid 

bodies (in this case, the probe and the surface) and 3 denotes the intervening 

medium. With this method, there is great potential for error. Care 

must be taken when calculating surface forces from adhesion measurements. 

Interactions not present at long range may be present when contact 

is made, such as solvation forces as well as the effects of roughness 

and deformations. In one study [23], both long-range forces and adhesion 

measurements were observed between latex spheres and glass surfaces 

in aqueous solution using the colloidal probe technique. Adhesion values 

were estimated on the basis of the long-range interaction forces. These 

calculated adhesion values were approximately 20–30 times greater than 

the adhesion values actually measured. 

2.3.2 Electrical double layer Forces 

As stated above, van der Waals interactions between identical particles 

are always attractive. If this was the only force present between colloidal 

particles in solution, then dispersions would be unstable due to aggregation, 

leading to the formation of a precipitate. Fortunately, this is not the 

case as particles in water or any liquid of high dielectric constant usually 

possess charges on their surfaces. Repulsion between identically charged 

particles is long range in character and is often sufficient to overcome the 

aggregating effects of attractive van der Waals interactions. 

2.3.2.1 The Electrical Double Layer 

From observations of colloidal systems, it can be concluded that particles 

dispersed in water or any liquid with a high dielectric constant will 

usually develop a surface charge. The charging of a surface in a liquid 

can be brought about by one of two charging mechanisms [2]: 

1. By the ionisation or dissociation of surface groups, which leaves 

behind a charged surface (e.g. the dissociation of protons from carboxylic 

acid groups, which leaves behind a negatively charged surface).


2. By the adsorption (binding) of ions from solution onto a previously 

uncharged surface. The adsorption of ions from solution can also 

occur onto oppositely charged sites, also known as ion exchange. 

Since the system as a whole is electrically neutral, the dispersing 

medium must contain an equivalent charge of the opposite sign. These 

charges are carried by ions, i.e., by an excess of ions of one sign on the 

particle surface and an excess of ions of the opposite sign in the solution. 

Hence, if we consider an individual particle immersed in the liquid, it is 

surrounded by an electrical double layer. One part of this double layer is 

formed by the charge of the surface of the particles. Another part of the 

electrical double layer is formed by the excess of oppositely charged ions 

in the solution. As a result of their thermal motion, the electrical charge 

carried by this layer extends over a certain distance from the particle surface 

and dies out gradually with increasing distance (diffuse layer) into 

the bulk liquid phase. 

2.3.2.2 Distribution of Electrical Charge and Potential in the 

Double Layer 

The first approximate theory for the electrical double layer was given by 

Gouy, Chapman, Debye and Hückel [24]. In this theory, the average charge 

distribution and the corresponding electrical potential function have been 

related on the basis of the Poisson–Boltzmann equation (PBE) [18]: 

∇ 2 �1 0 �zie� 

� � ni zie exp 

ε ε 

k T 

⎛ ⎞ 

⎜ ∑ ⎜ 

⎝⎜ 

⎠⎟ 

0 

r 

i 

B 

(2.27) 

where � is the electrical potential, n i 0 is the number density of ions of 

valency z i, k B is the Boltzmann constant, T is the absolute temperature, 

�ε 0 is the permittivity of vacuum, ε r is the dielectric constant of the background 

solvent and e is the elementary charge. 

The above PBE has been deduced using a number of simplifying 

assumptions that the electrolyte is an ideal solution with uniform 

dielectric properties, the ions are point charges and the potential of 

mean force and the average electrostatic potential are identical. Besides, 

the PBE is only applicable to the system with a symmetrical electrolyte 

or a mixture of electrolytes of the same valency type. According to this 

theory, the average charge density at a given point can be calculated 

from the average value of the electrical potential at the same point with 

Boltzmann’s theorem. The electrical potential distribution can be related 

to the charge density with the aid of Poisson’s equation. As a matter of 

fact, the Gouy–Chapman theory has a rather serious defect, which is 

mainly a consequence of the neglect of the finite dimensions of the ions.


In dilute solutions, where the extension of the diffuse layer is considerable, 

this neglect is to some degree permissible; but in more concentrated 

electrolyte solutions, the picture in terms of the Gouy–Chapman model 

becomes incorrect in some essential details. 

Stern [25] modified the Gouy–Chapman model by taking into consideration 

the finite size of real ions, underlying the double layer theory for 

a solid wall by dividing the charges in liquid into two parts. One part is 

considered as a layer of ions adsorbed to the wall, and is represented in 

the theory by a surface charge concentrated in a plane at a small distance, 

d, from the surface charge on the wall, also known as the outer Helmholtz 

plane (OHP), as shown in Figure 2.4. The second part of the liquid charge 

is then taken to be a diffuse space charge, as in the old theory, extending 

from the OHP at x � d to infinity, where the PBE can be applied. 

The method with which the distance to the OHP is calculated depends 

on the type of model used for describing the compact region. For an 

oxide surface, such as typically found on the surface of silica, a triple 

layer model such as the Gouy–Chapman–Grahame–Stern model [26] is 

often used to describe the compact region; see Figure 2.4(a). This model 

allows for a plane of adsorbed ions (partially dehydrated) on the particle 

surface (the centres of which form the locus for the inner Helmholtz 

plane (IHP)) followed by a plane occurring at the distance of closest 

approach of the hydrated counterions (the OHP). This is the mechanism 

by which the high surface charge on the oxide is reconciled with the quite 

low diffuse double layer potentials (zeta potentials). For other types of 

– 

– 

– 

Particle 

surface 

– 

– 

– 

ε r1 

IHP 

+ 

+ 

+ 

ε r2 

OHP 

+ 

Aqueous 

solution 

x = 0 i d 

ψ = ψo ψi ψd 

σ = σo σi σd A B 

– 

– 

– 

Particle 

surface 

– 

– 

– 

x = 0 

ψ = ψo 

σ = σ o 

εr 1 

OHP 

+ 

+ 

+ 

d 

ψd 

Aqueous 

solution 

FIGuRE 2.4 Models for compact part of the double layer: (A) Gouy–Chapman– 

Grahame–Stern (triple layer) model and (B) modified Gouy–Chapman model. 

σ d

surfaces such as proteins, where there are few or no adsorbed ions at all, 

the modified Gouy–Chapman model [26], where the OHP is located at 

the plane of closest approach of the hydrated counterions, is probably 

more appropriate; see Figure 2.4(b). The distance to the OHP can be calculated 

from the knowledge of the ionic crystal and hydrated ionic radii. 

The non-linear PBE is used to calculate the potential distribution 

inside the diffusive part of the electric double layer between two surfaces 

[18, 26]. According to the non-linear PBE, the aqueous solution is 

defined by its static dielectric constant only. The surface charge is usually 

taken as averaged over the surface, and the discrete nature of ions is not 

considered. 

In order to calculate the potential distribution around a particle, not 

only is the PBE needed, but the boundary conditions also have to be 

specified. A choice of boundary conditions is available at the particle surface. 

It is important to choose physically meaningful conditions at the 

particle surfaces, which depend on the colloidal material being considered 

(see next section). 

2.3.2.3 Interaction Forces Between Double Layers 

Analytical Solutions When two like-charged particles approach each 

other, their electrical double layers will begin to overlap, resulting in a 

repulsive force that will oppose further approach. For very dilute systems 

where just two particles can be considered in the interaction, it is possible 

to obtain analytical expressions for the calculation of the repulsive interaction 

energy between two spherical particles on the basis of the interaction 

energy equations derived for infinite flat plates of the same material 

with either the Derjaguin approximation [1] or the linear superposition 

approximation (LSA) [27], as shown below. 

V 


R � 

128 1 2 

1 2 

πa 

a n�kT � � 

( a � a ) � 

2 1 2 

exp( �κD) 

(2.28) 

where D is the surface-surface separation between the particles; a 1 and a 2 

denote the radii of particles 1 and 2; � is the Debye–Hückel reciprocal 

length; n o is the bulk density of ions and � is the reduced surface potential, 

which can be expressed as: 

� 

i 

⎛ze�i 

⎞ 

� tanh⎜ ⎝⎜ 

4kT 

⎠⎟⎟ 

(2.29) 

The above equation is valid only when both the conditions �a � 5 and 

D � � a are satisfied. There are many other expressions available on the 

basis of various assumptions for the sphere-sphere double layer interaction


energy. For further information, readers are referred to the literature 

[44–49]. In general, the LSA method yields the correct interaction at large 

separations for all surface potentials and particle sizes; Derjaguin’s integration 

gives accurate results for large particles at short distances and the 

McCartney and Levine formulation [33] is a good approximation at all 

separations except for small potentials. It should be noted that although 

the first two methods themselves place no restriction on the potentials, 

the resulting expressions often do because of the difficulty in solving the 

PBE. Therefore, care must be taken in choosing the correct expression. 

Numerical Solutions The previous analytical solutions only apply for 

a limited range of ionic strength, size and separation distance. This is 

mainly due to the fact that, for most cases, no exact analytical solution of 

the PBE is available. These limitations may be removed by considering 

numerical solutions of the problem being investigated. 

Before the advent of modern computers, a few numerical solutions for 

the PBE around a sphere were worked out [34]. A more extensive tabulation 

was compiled by Hoskin [35] using electronic computing techniques. 

Loeb et al. [36] then compiled a much more comprehensive set of tables, 

covering a wide variety of electrolyte types, concentrations and surface 

potentials. More recently, the PBE has been solved by various methods 

for unconfined [37–45] and confined [39, 46, 47] particles. These simulations 

can be multidimensional, and include Runge–Kutta, finite-element, 

finite difference and substitution methods. The case of two interacting 

particles isolated in a dielectric medium is usually considered as a test 

case for any new solution method as this system has been solved previously 

by many authors (e.g. see [38, 40–44]). 

As mentioned in Section 2.3.2.2, the PBE needs to be solved with 

respect to a set of boundary conditions. As an example, consider the case 

of an isolated sphere. The charge distribution of the counterions away 

from the particle is described by the non-linear PBE in spherical coordinates 

as: 

2 

d � 2 d� 

2n 

ze ez� 

� � sinh 

2 

dr r dr ε ε kT 

⎛ ⎞ 

⎜ 

⎝⎜ 

⎠⎟ 

0 

o 

r 

(2.30) 

Equation (2.30) cannot be solved analytically; so in order to solve the 

PBE numerically, two boundary conditions will be required. The condition 

that is used at the outer boundary is that of electroneutrality, given as: 

d� 

dr 

r�∞ 

�0 

(2.31)


A choice of boundary conditions is available at the particle surface. It 

is important to choose physically meaningful conditions at the particle 

surface, which may depend on the colloidal material being considered. 

For metal sols in a solution, a constant surface potential boundary condition 

is appropriate, given by: 

� o r� � 

α 

constant 

(2.32) 

where � is the particle radius plus the distance to the OHP (� a � d) 

(see Figure 2.4). 

A constant surface charge boundary condition may be appropriate 

when the surface charge is caused by crystal lattice defects, such as in 

clay minerals. 

� � ε ε � 

o d r o 

d 

�� constant 

dr 

r�α 

(2.33) 

A boundary condition where the zeta potential is held constant is also 

possible [37, 48]. 

� d r=α 

� ζ � constant 

(2.34) 

In the case of biomaterials and oxide surfaces, the charge can be generated 

by surface dissociation reactions, which are influenced by the solution 

conditions. This can be described by a boundary condition known as 

charge regulation [49]. 

� � f ( � ) ≠ constant 

o o 

(2.35) 

As an example of this, consider the protein bovine serum albumin 

(BSA). The protein is made up of a number of different types of amino 

acids. Only certain amino acids will take part in the ionisation reactions, 

which will generate a charge on the protein surface. The development of 

a charge regulation model for BSA requires the number of these chargegenerating 

amino acids to be known. This data is available in the literature 

from the amino acid sequence of the protein [50] or from titration 

data [51]. The relevant equilibria reactions are illustrated by: 

1 

� � 

for aspartic or glutamic acid � COOH �� 

� COO � H (2.36) 

2 

for lysine � NH �� 

� NH � H 

K 

� K 

� 

3 2 

(2.37)


Considering equation (2.36) as an example, the equilibrium constant 

for the reaction may be written as: 

K 

1 � 

ˆ 

� 

s 

[ COO ][ H ] 

[ COOH] 

(2.38) 

where [H � ] s is the hydrogen ion concentration at the BSA surface, which 

can be determined from: 

� + ⎛�ze 

o 

[ H ] s � [ H ] bulk exp⎜ 

� ⎞ 

⎝⎜ 

kT ⎠⎟ 

(2.39) 

with the bulk hydrogen ion concentration being found from the pH of 

the dispersion. 

Now, let 

R 

K1 

[ H ] 

� � 

s 

⎛ 

ˆ 

[ COO ] ⎞ 

⎜ 

⎜˜ 

⎝⎜ 

[ COOH] 

⎠⎟ 

then, the fraction of carboxyl groups ionised, X COO, will be: 

X 

COO ˆ 

ˆ 

COO 

COOH COO R 

[ ] 

� 

� 

ˆ 

[ ] � [ ] 1�R 

(2.40) 

(2.41) 

The number of surface charges generated on the BSA surface owing to 

the ionisation of the carboxyl groups can then be found via: 

Z ˆ � X ˆ � Total number of carboxyl groups on BSA surface (2.42) 

COO COO 

Similar calculations can be performed for the other amino acids and 

the total charge number due to the acid–base equilibria on the BSA surface 

can then be found. 

ZAB � ∑ �� ∑ �� 

(2.43) 

To solve these equations, the pK a values of the amino acid groups in 

their environment at the BSA surface need to be known. The pK a values 

for the amino acid groups on BSA are available in the literature [51, 52]. 

If this data were not available for the specific protein being investigated, 

general data is available in the literature for the intrinsic pK a values of 

the ionisable amino acid groups found in proteins [52]. These pK a values 

can be substantially different from the pK a values of the free amino acids. 

The above equations have shown how the complex acid–base equilibria 

of the amino acid surface groups may be described, but the average

net molecular charge of the BSA molecule will also depend on whether 

some surface groups on the molecule will also be involved with ionic 

equilibria with other ions in the electrolyte solution. For BSA, chloride 

binding will occur [53]. This chloride binding may be described by [54]: 

Z 

Cl 

� � 

( ) 

( ) 

� �zeψ 

440 � [ Cl ] exp o 

kT 

� �zeψ 

1� 44 � [ Cl ] exp o 

kT 


� 

�zeψo 

( kT) 

�zeψo 

( kT 

33 γ[ 

Cl ] exp 

� 

� 

1�1. 1 γ [ Cl ] exp ) 

(2.44) 

where � is the activity coefficient of the chloride ion at the particle surface 

(determined from activity coefficient data for NaCl solutions). 

Therefore, the overall surface charge number of a BSA molecule is: 

Z T �Z AB �Z � 

Cl 

(2.45) 

When solving the PBE using charge regulation as a boundary condition, 

the compact part of the double layer around the BSA molecule needs 

to be taken into account. Figure 2.4(b) illustrates the model assumed 

for the compact part of the double layer. This model can be termed the 

Zeroth-order Stern model [55], as we have a zone of thickness, d, that is 

devoid of ions and represents a distance of closest approach to the particle 

surface of charge density � o. From electroneutrality, 

�o �� d 

From the solution of the PBE, � d can be determined as: 

� ε ε � d 

d � o r 

dr 

r�a� d 

(2.46) 

(2.47) 

The surface potential of the particle, � o, may also be determined by 

allowing for the capacitance of the fluid in the compact layer around the 

sphere. For two concentric spheres, the capacitance, C, may be determined 

using [56]: 

aα 

C � 4πεoεr α � a 

(2.48) 

where a is the radius of the inner sphere and � (� a � d) is the radius of 

the outer sphere. 

The capacitance can also be evaluated from the surface charge density as: 

C Q 

2 

4πa 

�o 

� � 

∆V 

� � � 

o d 

(2.49)


Combining equations (2.48) and (2.49), 

� 

o 

oad 

� 

ε ε a d 

� 

� � 

� 

( ) 

o r 

d 

(2.50) 

The surface potential can therefore be established if a, d, �d, �o, �εo and εr are known. The value for the dielectric constant for the compact layer, εr, is unknown, but for the model used here, it has been shown that the bulk 

dielectric constant for water may be used if d is in the range 0.1–0.3 nm 

[55]. Thus, from an initial guess for �d, �d (and thus �o) may be deter- 

mined from the solution of the non-linear PBE (which gives d dr r a d 

�/ � � ). 

From these values, the surface potential, � o, can be evaluated from equation 

(2.50) and then the number of charges on the BSA molecule may be 

determined from the charge regulation model. Using Z T, a value for the 

surface charge density may be recalculated. 

� 

o 

ZT e 

� 

2 

4πa 

(2.51) 

The two values for the surface charge calculated, via the PBE and the 

surface charge model, may then be compared for a given � d and an iteration 

may be performed on � d until the surface charge calculated via both 

methods is equivalent. In this way, for given dispersion conditions (pH, 

ionic strength, concentration), the value of the potential at the OHP may 

be determined. This potential is widely considered to be the zeta potential 

of the molecule [57]. The calculated value of the zeta potential may 

be compared to the value obtained experimentally from electrophoresis 

measurements on dilute BSA dispersions [58]. 

Once the PBE has been solved, calculation of the interaction energy 

may be performed using an appropriate model. 

In the case of concentrated colloidal dispersions, however, the interaction 

energy between particles (as in a gel layer) is multiparticle in nature, 

so modification of the two-body interaction has to be made in order to 

allow for multiparticle interactions. A method by which the multiparticle 

nature of such interactions can be taken into account is to use a cell 

model [59] combined with a numerical solution of the non-linear PBE 

in spherical coordinates [60–64]. This cell model is based on the Wigner 

and Seitz cell model [65] that approximated the free electron energy of a 

crystal lattice by calculating the energy of a single crystal, since it has the 

same symmetry as the lattice. 

The concentrated colloidal dispersion can now be considered as being 

divided into spherical cells so that each cell contains a single particle and 

a concentric spherical shell of an electrolyte solution, having an outer 

radius of certain magnitude such that the particle cell volume ratio in 

the unit cell is equal to the particle volume fraction throughout the entire

suspension, and the overall charge density within the cell is zero (electroneutral). 

This kind of approach gives a mean field approximation that 

accounts for multiparticle interactions to yield the configurational electrostatic 

free energy per particle [78]. By equating the configurational free 

energy with the pairwise summation of forces in hexagonal arrays, an 

expression for the repulsive force between two particles can be obtained, 

which implicitly takes into account the multiparticle effect [60]. 

1 ⎛ ⎛ 

o ze�β ( D) 

⎞ ⎞ 

FR ( D) � Sβ ( D) n kT ⎜ 

⎜cosh 

⎜ � 1 

3 ⎝⎜ 

⎝⎜ 

kT ⎠⎟ 

⎠⎟ 

(2.52) 

where S�(D) is the surface area of the spherical cell around the particle, 

no is the ion number concentration, z is the valence of the ions, e is the 

elementary electronic charge and ��(D) is the potential at the surface of 

the spherical cell. 

In order to evaluate the above equation, the size of the cell and the 

potential at the cell surface need to be known. The radius of the fluid 

shell can be determined with the volume fraction approach [62]. The 

potential at the outer boundary of the cell may be determined by solving 

the non-linear PBE in spherical coordinates numerically, using the electroneutrality 

boundary condition at the cell surface (i.e. d�/ dr r�β 

� 0) 

and the appropriate boundary condition at the particle surface. 

The interaction energy may now be determined using: 

V ( D) � � F ( D) dD 

R 

∫ 

D 

∞ 

R 

(2.53) 

This interaction energy implicitly takes multiparticle interactions into 

account. 

2.3.3 dlVo theory 


DLVO theory is named after Derjaguin and Landau [66] and Verwey 

and Overbeek [24], who were responsible for its development during 

the 1940s. This theory describes the forces present between charged surfaces 

interacting through a liquid medium. It combines the effects of the 

London dispersion van der Waals attraction and the electrostatic repulsion 

due to the overlap of the double layer of counterions. The central 

concept of the DLVO theory is that the total interaction energy of two 

surfaces or particles is given by the summation of the attractive and 

repulsive contributions. This can be written as: 

VT � VA � VR 

(2.54)


where the total interaction energy V T is expressed in terms of the repulsive 

double layer interaction energy V R and the attractive London–van 

der Waals energy V A. For a measurement made between a spherical colloid 

probe and a plain surface, this can be adapted to give the relationship 

for a normalised force: 

F 

R 

�2π( V � V ) 

A R 

(2.55) 

Contrary to the double layer interaction, the van der Waals interaction 

energy is mostly insensitive to variations in electrolyte strength and pH. 

Additionally, the van der Waals attraction must always be greater than 

the double layer repulsion at extremely small distances since the interaction 

energy satisfies a power law (i.e. V A � � D �n ), whereas the double 

layer interaction energy remains finite or increases far more slowly 

within the same small separation range. 

DLVO theory was challenged by the existence of long-range attractive 

electrostatic forces between particles of like charge. The established theory 

of colloidal interactions predicts that an isolated pair of like-charged 

colloidal spheres in an electrolyte should experience a purely repulsive 

screened electrostatic (Coulombic) interaction. The experimental evidence, 

however, indicates that the effective interparticle potential can 

have a long-range attractive component in more concentrated suspensions 

[67, 68] and for particles confined by charged glass walls [69, 70]. 

The explanations for the observation are divided and debatable. One of 

the arguments [71] demonstrated that the attractive interaction measured 

between like-charged colloidal spheres near a wall can be accounted for 

by a non-equilibrium hydrodynamic effect, which was proved by both 

analytical results and Brownian dynamics simulations. 

2.3.3.1 Measurement of DLVO Forces Using Atomic Force Microscopy 

The following section will review a number of papers describing 

experiments to measure van der Waals and electrostatic double layer 

forces between particles using the colloidal probe technique, but should 

not be considered as a complete coverage of published information. For 

further reading, there are a number of excellent reviews that may be recommended 

[13, 21, 72–74]. 

The first use of AFM to measure interactions between a colloidal particle 

and a surface was reported by Ducker and colleagues, where a silica 

sphere was allowed to interact with a silica surface in aqueous NaCl 

solutions [4, 75]. Force measurements were fitted with theoretical force 

laws for DLVO theory, combining van der Waals and electrostatic double 

layer interactions. For separations greater than 3 nm, observations agreed 

favourably with the conventional DLVO theory. However, at closer


separations, deviations did occur. This was attributed by the authors to 

an effect of the roughness of the surfaces involved, leading to a deviation 

from the assumed idealised geometry. 

There are a number of examples of the AFM being used along with the 

colloidal probe technique to probe van der Waals interactions between 

surfaces in a variety of media. Whilst most such studies examine a combination 

of van der Waals along with other surface forces, there are a few 

that concentrate on van der Waals measurements. Milling and colleagues 

[76] observed the interactions between colloidal gold spheres and poly(tetrafluoroethylene) 

(PTFE) surfaces in a variety of different liquids. Hamaker 

constants were found by fitting the appropriate force laws to the experimental 

data. As noted by the authors, the experimentally determined 

values for the Hamaker constant were only in agreement qualitatively 

with those calculated from theory. In addition, theoretical values varied 

significantly, depending upon whether an amorphous or crystalline form 

of PTFE was considered. For the majority of liquids used, which were of 

a polar nature (water, ethanol and dimethyl sulfoxide), only attractive 

forces were measured. In the case of dimethyl formamide, which was also 

a polar molecule, only repulsive interactions were observed. For these 

interactions, only water had been expected to show an attractive interaction. 

The authors concluded that in the case of the other polar liquids 

studied that showed attraction, the surfaces must have become contaminated 

by charged groups, leading to interactions that were not purely of 

a van der Waals nature. For interactions taking place in the perfluoroalkanes 

perfluorohexane and perfluorocyclohexane, as well as in air, shortrange 

interactions were also attractive. This was as predicted from theory, 

but the authors were unable to obtain experimentally determined values 

for A H. In the other low-polarity solvents examined (cyclohexane, dodecane, 

p-xylene and bromobenzene), all interactions were found to be repulsive, 

which was qualitatively in accordance with theoretical A H values calculated 

assuming amorphous PTFE surfaces. 

Karamen et al. [77] studied the interactions between model aluminium 

oxide surfaces in 1 mM solutions of potassium chloride as a function of 

pH. At separation distances greater than 5 nm, interaction forces were 

described very well by the traditional DLVO theory. From calculations 

of the surface potential from forces measured using DLVO theory, it was 

possible to calculate an isoelectric point at approximately pH 7, which 

was in agreement with values obtained from the literature. 

Many colloidal systems consist of particles with self-assembled monolayers 

covalently bound to the surface. Such a system is inherently more 

complex than those having interactions between single materials, as if the 

outer layer is thin, then interactions between the underlying surfaces will 

occur as well as between the monolayers. Kane and Mulvaney [78] studied 

the interactions between gold spheres and surfaces before and after


the deposition of mercaptoundecanoic acid (MUA). Force measurements 

at different electrolyte concentrations and pH values were fitted with a 

modified DLVO theory to determine surface potentials and Hamaker 

constants. The adsorption of the MUA itself was found to substantially 

decrease the magnitude of the dispersive forces between the gold surfaces. 

It was also found that the degree of ionisation of the surface carboxy 

groups was very low. The authors applied two models to explain 

these results. It was concluded that either a thicker-than-usually-expected 

Stern layer was present or that strong competitive binding of cations was 

the cause. Surface interactions between particles and surfaces with more 

complex attached monolayers, such as proteins, have also been investigated. 

Bowen et al. [79] investigated systems of silica microspheres and 

surfaces co-incubated to give an adsorbed layer of bovine serum albumin 

(BSA) at different values of pH and NaCl concentrations. Figure 2.5 

shows a plot of representative force curves obtained as a BSA-coated 

silica sphere approached a BSA-coated silica surface in aqueous NaCl 

solutions of differing ionic strengths. As the ionic strength was increased, 

both the range and magnitude of repulsive interactions increased. For 

the three highest NaCl concentrations, experimental observations were 

in good agreement with the values predicted from DLVO theory and zeta 

potential values. The zeta potentials for the BSA were calculated using a 

site-dissociation-site-binding approach from the amino acid sequence [58, 

80]. At the lowest ionic strength examined (0.0002 M NaCl), the observed 

values were higher than those predicted from theory. 

Normalised force, F/R (mN/m) 

1 

0.1 

0.01 

0.0001 

0 5 10 15 20 25 30 

Distance [nm] 

FIGuRE 2.5 Plot of normalised force versus separation distance plot for silica surfaces 

coated with monolayers of BSA at four concentrations of NaCl at pH 8.0: (�) 0.1 M; (�) 0.01 M; 

(�) 0.001 M; (�) 0.0002 M. The lines are theoretical predictions from DLVO theory.

Interaction between colloidal particles and filtration media is of much 

interest industrially, due to the propensity of dispersed particles to foul 

membrane surfaces and reduce their efficiency [81, 82]. As under conditions 

in which membrane filtration most often occurs both the membrane 

and dispersed colloids and other particles carry surface charges, 

the strength and sign of electrical double layer interactions are of great 

importance. The forces involved in the approach of a colloidal particle to 

a membrane surface are essentially a balance between electrical double 

layer interactions and hydrodynamic forces. Studies have been made of 

double layer interactions using model silica colloidal spheres and polymeric 

microfiltration membranes [83]. Solutions of NaCl were prepared 

of varying ionic strengths at a single pH value (pH 8.0). Representative 

force curves for each approach made by the silica probe to membrane surfaces 

are shown in Figure 2.6. At all ionic strengths, forces were significantly 

repulsive at all separation distances, showing that the electrostatic 

double layer repulsion is dominant in all cases. The range that the repulsive 

interactions first become detectable increased from approximately 

10 nm at 10 �1 M NaCl to approximately 35 nm at 10 �4 M. When measurements 

were made in high purity water, this increased to 60 nm. The 

change in the magnitude of the forces with decreasing ionic strength is 

in accordance with electrical double layer theory, with the decay lengths 

of the measured force curves comparable to the Debye charge screening 

lengths of the different ionic strength solutions under study. The decrease 

F/R [mN/m] 

20 

15 

10 

5 


10�3 10 

M NaCl 

�2 10 

M NaCl 

�1 M NaCl 

10 �4 M NaCl 

0 

0 5 10 15 20 25 30 35 40 45 

Distance [nm] 

FIGuRE 2.6 Plot showing normalised force versus separation distance for the approach 

of a silica colloid probe towards a microfiltration membrane surface at different salt concentrations. 

As the concentration of NaCl is increased, repulsive forces on approach decrease 

owing to charge screening effects.


in repulsive interaction between the particles and the membrane with the 

increase in the salt concentration has implications for membrane filtration 

processes, but especially for the desalination treatment of water. Brant and 

Childress [84] studied the long-range interaction forces between colloids 

of a variety of materials (silica, alumina and polystyrene) with reverse 

osmosis membranes and developed an extended DLVO theory that added 

the effect of acid–base interactions, with AFM experiments used to validate 

the extended theory. It was found that for interactions between two 

hydrophilic surfaces, the extended theory fitted the data better than classical 

theory, demonstrating the importance of acid–base interactions for 

this configuration. For interactions between hydrophobic materials, the 

extended theory was not significantly different from the classical theory, 

as would be expected for interactions between non-polar materials. 

2.3.4 Solvation Forces 

The DLVO theory successfully explains the long-range interaction 

forces observed in a large number of systems (colloids, surfactant solutions, 

lipid bilayers etc.) in terms of the electrical double layer and 

London–van der Waals forces. However, when two surfaces or particles 

approach closer than a few nanometres, the interactions between two solid 

surfaces in a liquid medium fail to be accounted for by DLVO theory. This 

is because the theories of van der Waals and double layer forces discussed 

in the previous sections are both continuum theories, described on the 

basis of the bulk properties of the intervening solvent such as its refractive 

index, dielectric constant and density, whereas the individual nature 

of the molecules involved, such as their discrete size, shape and chemistry, 

was not taken into consideration by DLVO theory. Another explanation 

for this is that other non-DLVO forces come into play, although the 

physical origin of such forces is still somewhat obscure [85, 86]. These 

additional forces can be monotonically repulsive, monotonically attractive 

or even oscillatory in some cases. And these forces can be much stronger 

than either of the two DLVO forces at small separations [2, 87]. 

To understand how the additional forces arise between two surfaces a 

few nanometers apart, we need to start with the simplest but most general 

case of inert spherical molecules between two smooth surfaces, first 

considering the way solvent molecules order themselves at a solid–liquid 

interface, then considering how this structure corresponds to the presence 

of a neighbouring surface and how this in turn brings about the shortrange 

interaction between two surfaces in the liquid. Usually, the liquid 

structure close to an interface is different from that in the bulk. For many 

liquids, the density profile normal to a solid surface oscillates around 

the bulk density, with a periodicity of a molecular diameter in a narrow 

region near the interface. This region typically extends over several


molecular diameters. Within this range, the molecules are ordered in layers 

according to some theoretical work and particularly computer simulations 

[88, 89] as well as experimental observations [90, 91]. When two 

such surfaces approach each other, one layer of molecules after another is 

squeezed out of the closing gap. The geometric constraining effect of the 

approaching wall on these molecules and attractive interactions between 

the surface and liquid molecules hence create the solvation force between 

the two surfaces. For simple spherical molecules between two hard, 

smooth surfaces, the solvation force is usually a decaying oscillatory 

function of distance. For molecules with asymmetric shapes or whose 

interaction potentials are anisotropic or not pairwise additive, the resulting 

solvation force may also have a monotonically repulsive or attractive 

component. When the solvent is water, they are referred to as hydration 

forces. Solvation forces depend both on the chemical and physical properties 

of the surfaces being considered, such as the wettability, crystal 

structure, surface morphology and rigidity and on the properties of the 

intervening medium. 

The hydration force is one of the most widely studied and controversial 

non-DLVO forces, a strong short-range force that decays exponentially 

with the distance, D, between the surfaces [92, 93]: 

F ( D) � Ke 

SOL 

� D/ l 

(2.56) 

where K � 0 relates to the hydrophilic repulsion forces, K � 0 relates to 

the hydrophobic attraction forces and l is the correlation length of the orientational 

ordering of water molecules. 

The concept of the hydration force emerged to explain measurements 

of forces between neutral lipid bilayer membranes [93]. Its presence in 

charged systems is controversial, but there is experimental evidence of 

non-DLVO forces following equation (2.56) in systems as diverse as 

dihexadecyldimethyl ammonium acetate surfactant bilayers [94], DNA 

polyelectrolyte solutions [95] and charged polysaccharides [96]. In these 

experiments, the hydration forces show little sensitivity to ionic strength. 

Many theoretical studies and computer simulations of various confined 

liquids, including water, have invariably led to a solvation force 

described by an exponentially decaying cos-function of the form 

[97–100]: 

⎛ πD⎞ 

FSOL ( D) � f0cos 

⎜ e 

⎝⎜ 

� ⎠⎟ 

2 �D/ 

D0 

m 

(2.57) 

where F SOL is the force per unit area; f 0 is the force extrapolated to separation 

distance, D � 0; � m is the molecular diameter and D 0 is the characteristic 

decay length.


A repulsive force dominant at short ranges between silica surfaces in 

aqueous solutions of NaCl has been reported by Grabbe and Horn [101], 

which was also found to be independent of electrolyte concentration over 

the range investigated. They attributed this force to a hydration repulsion 

resulting from hydrogen bonding of water to the silica surface, and fitted 

the additional component to a sum of two exponentials to work out the 

formula for the hydration forces in the system. 

The physical mechanisms underlying the hydration force are still a 

matter for debate. One possible mechanism is the anomalous polarisation 

of water near the interfaces, which completely alters its dielectric 

response [102–104]. These theories imply an electrostatic origin of the 

hydration force. However, other authors report [105] that there is no 

evidence for a significant structuring of water layers near interfaces, or 

a perturbation of its dielectric response, as envisaged by previous theories. 

Instead, they suggest that the repulsive forces are due to entropic 

(osmotic) repulsion of thermally excited molecular groups that protrude 

from the surfaces [106]. This theory explains many experimental observations 

in neutral systems [107], but its validity in charged systems is not 

certain. Given the available evidence from experiments and simulations, 

it is not possible to reach a definitive conclusion on the precise role of 

these mechanisms in determining the hydration forces. Until recently, 

computer simulations of water films coated with ionic surfactants 

showed that protrusions are not significant in these systems [108]. On 

the other hand, computer simulations show that water has an anomalous 

dielectric behaviour near charged interfaces [109], but the observed electrostatic 

fields obviously differ from the predictions of electrostatic theories 

on hydration forces [103, 110]. The effect of this anomalous dielectric 

behaviour of water on the electrostatic force between surfaces or interfaces 

is still unknown. 

The use of AFM to measure solvation forces between surfaces has been 

of some interest amongst researchers in recent years for the purposes of 

both studying the phenomena between closely interacting probes and 

surfaces that may cause artefacts when imaging with an AFM and investigating 

the effect of these solvation forces on the interactions between 

colloidal particles. O’Shea and colleagues [111] observed an oscillatory 

force on close approach of a sharp AFM probe to a graphite surface in 

water, octamethylcyclotetra siloxane (OMCTS), and dodecanol. A series 

of repulsive barriers were observed as approach was made for OMCTS 

and dodecanol, with each repulsive barrier becoming successively larger, 

owing to the closer-bound solvation layers becoming harder to displace. 

The authors calculated that the energy required to remove the solvation 

molecules was 5–25 times kT for OMCTS and 5–1000 times kT for 

dodecanol, suggesting that only a small number of molecules were being 

displaced. In addition, it was noted that the distance between successive


oscillatory peaks compared well with the sizes of the molecules of interest, 

suggesting that each solvation shell consisted of a single layer of 

molecules. A later set of measurements in OMCTS and dodecanol on 

HOPG reached a similar conclusion [112, 113]. No displacement of solvation 

layers could be observed in water owing to the relatively large range 

and magnitude of the attractive jump-in event observed. In a later set of 

experiments [114], an oscillating lever was used to probe the solvation 

forces in OMCTS and dodecanol, allowing the mechanical compliance of 

the solvation shells to be measured. Here, periodic changes in the amplitude 

of lever oscillations were observed, which was explained as being 

because of an increase in the effective viscosity of the solutions when the 

surfaces were in close approach. It was noted that the presence of oscillatory 

structural forces even at the highly curved geometries present, even 

when using a sharp AFM probe, could have a detrimental influence on 

the very high resolution imaging of surfaces when using AFM. 

Solvation forces were measured in primary alcohols between silicon 

nitride probes and mica and HOPG surfaces by Franz and Butt [115]. For 

the measurements made against the hydrophilic mica, no solvation oscillation 

forces were observed at separation distances of less than 4 nm. At 

distances less than this, repulsive maxima followed by sudden jump-in 

events were observed. These repeated maxima were ascribed to the presence 

of solvation shells, with at least two of these layers present. These 

solvation forces were determined to be greater in magnitude than the 

attractive van der Waals forces present. It was noted that the period of 

the force oscillations increased linearly with chain length, with the period 

greater than the chain length. It was concluded that for the measurements 

made on mica, the molecules did not take on a flat conformation, 

but were at least partially upright. On the hydrophobic HOPG surface, 

measurements in 1-propanol and 1-pentanol oscillations had a period 

of 0.45 nm, suggesting that on the hydrophobic surface they did lie flat 

against the surface. 

Valle-Delgado and colleagues [116] investigated the solvation forces 

in water between hydrophilic silica spheres versus plane silica surfaces. 

A repulsive force was measured (�2 nm) at ranges shorter than the 

observed double layer repulsion and attractive van der Waals forces. 

A number of theoretical models were applied to the experimental data 

and it was concluded that for the situation under investigation, the observations 

were best explained by the formation and rupture of hydrogen 

bonds between SiOH groups on the silica surfaces and a single layer of 

water molecules. 

Jarvis et al. [117] used a carbon nanotube to probe solvation forces in 

water against a self-assembled monolayer bound to a gold surface, which 

had been characterised by imaging using the nanotube probe. When the 

forces were normalised, they were found to be in reasonable agreement


with previous measurements undertaken with the surface force apparatus 

[118]. The authors concluded that the forces scaled along with the surface 

interaction dimensions between the mesoscale and nanoscale [117]. 

2.3.5 Steric Interaction Forces 

For molecules attached to a solid surface in a liquid environment, 

chains with a degree of freedom to move will tend to dangle out into the 

solution where they remain thermally mobile. On approach of two polymer-covered 

surfaces, the entropy of confining these dangling chains 

results in a repulsive entropic force, which, for overlapping polymer 

molecules, is known as the steric or overlap repulsion. In ancient Egypt, 

people already knew how to keep ink stabilised by dispersing soot particles 

in water, incubated with gum arabicum or egg-adsorbed polymers, 

which, in the first case, is a mixture of polysaccharide and glycoprotein 

and in the second mainly the protein albumin, which works through this 

steric repulsion. However, steric repulsion does not necessarily have to 

be due to polymeric molecules; layers of small molecules can have the 

same effect, albeit at a much shorter range. 

Steric stabilisation of dispersions is very important in many industrial 

processes. This is because colloidal particles that normally coagulate in 

a solvent can often be stabilised by adding a small amount of polymer 

to the dispersing medium. Such polymer additives are known as protectives 

against coagulation and they lead to the steric stabilisation of a colloid. 

Both synthetic polymers and biopolymers (e.g. protein, gelatine) are 

widely used in both non-polar and polar solvents (e.g. in paints, toners, 

emulsions, cosmetics, pharmaceuticals, processed food, soils, lubricants). 

Theories of steric interactions are not well developed. There is no simple, 

comprehensive theory available as steric forces are complicated and 

difficult to describe [119–121]. The magnitude of the force between surfaces 

coated with polymers depends on the quantity or coverage of polymer on 

each surface, on whether the polymer is simply adsorbed from solution (a 

reversible process) or irreversibly grafted onto the surfaces and finally on 

the quality of the solvent [119, 122]. Different components contribute to the 

force, and which component dominates the total force is situation specific. 

For interactions in poor and theta solvents, there are some theories 

available for low and high surface coverage. In the case of the low coverage 

where there is no overlap or entanglement of neighbouring chains, 

the repulsive energy per unit area is a complex series and roughly exponential 

[123–126]. As for the high coverage of end-grafted chains, the 

thickness of the brush layer increases linearly with the length of the polymer 

molecule. Once two brush-bearing surfaces are close enough to each 

other, there is a repulsive pressure between them, and this force can be 

approximated by the Alexander–de Gennes theory [119, 127, 128].

Studies of forces between model alumina surfaces in electrolyte solutions 

have noted the existence of steric interactions at basic (�8) pH, 

most probably due to the formation of a hydrated gel layer at the solid/ 

liquid interface [77, 129] providing an extra resistance to hard contact 

being made. At low pH values, the surface forces were described by classical 

DLVO theory, but at high pH with the presence of the hydrated gel 

layer, deviations from DLVO theory occurred at close separations. Polat 

et al. [129] measured frictional (lateral) forces in addition to forces normal 

to the surface. Differences in the normal forces at different pH values had 

a significant effect on the frictional forces. At pH values where the additional 

repulsive force due to hydration was present, the frictional forces 

were significantly decreased. The authors concluded that such behaviour 

was likely to have implications for the rheology stability and forming 

behaviour of powders made from this material and potentially for some 

other metal oxide materials. 

The adsorption of electrolyte and surfactant molecules from solution 

to solid surfaces is also likely to result in the addition of steric forces on 

close approach between surfaces. Studies of the surface forces between 

gold-coated silica spheres mounted on AFM cantilevers and plane gold 

surfaces in aqueous solutions of gold chloride, sodium chloride and trisodium 

citrate found that when the citrate and chloride anions were added 

together a short-range steric barrier appeared [130]. The range of this steric 

barrier was equal to the size of two citrate anions, suggesting that the 

citrate was coating each opposing surface with a monolayer. Meagher and 

colleagues studied the interactions between silica microspheres and �-alumina 

plane surfaces in the presence of different combinations of electrolyte, 

polyelectrolyte and surfactant [131]. In the presence of aqueous electrolyte 

alone, long-range forces compared well with DLVO theory at all separations. 

At high pH values, all forces measured were repulsive. As the pH 

was decreased, the repulsion was reduced, eventually starting to show features 

of attraction as pH was reduced to below the isoelectric point for the 

alumina (pH 5.5). When the polyelectrolyte sodium poly(styrene sulfonate) 

was added, with and without the presence of the cationic surfactant cetyltrimethylammonium 

bromate (CTAB) (at concentrations below its critical 

micelle concentration), at pH values equal to or higher than the isoelectric 

point of alumina, an additional repulsive force was observed at approaches 

of 3 nm or less. This deviation from the DLVO theory was observed as a 

short-range repulsive force that varied in its magnitude and range. 

2.3.6 Hydrophobic Interaction Forces 


A hydrophobic surface usually has no polar or ionic groups or hydrogen-bonding 

sites so that there is no affinity for water and the surface 

to bond together. Ordinary water in bulk is significantly structured


because of hydrogen bonding between the water molecules. The cooperative 

nature of this bonding [132] means that quite large clusters of 

hydrogen-bonded water molecules can form although they may continually 

form and break down in response to thermal energy fluctuations. 

The orientation of water molecules in contact with a hydrophobic molecule 

is entropically unfavourable; therefore, two such molecules tend 

to come together simply by attracting each other. As a result, the entropically 

unfavoured water molecules are expelled into the bulk and the 

total free energy of the system is reduced accordingly. The presence of 

a hydrophobic surface could restrict the natural structuring tendency 

of water by imposing a barrier that prevents the growth of clusters in a 

given direction. Similar effects occur between two hydrophobic surfaces 

in water. Water molecules confined in a gap between two such surfaces 

would thus be unable to form clusters larger than a certain size. For an 

extremely narrow gap, this could be a serious limitation and result in an 

increased free energy of the water in comparison with that in bulk. In 

other words, this would give rise to an attractive force between hydrophobic 

surfaces as a consequence of water molecules migrating from the 

gap to the bulk water where there are unrestricted hydrogen-bonding 

opportunities and a lower free energy. 

Attraction between hydrophobic surfaces has been measured directly 

[133] and can be of surprisingly long range, up to about 80 nm [134]. The 

attraction was much stronger than the van der Waals force and of much 

greater range. The interaction of filaments of hydrophobised silica was 

measured by Rabinovich and Derjaguin [135]. They found an attractive 

force at large separation distances, one to two orders of magnitude 

greater than van der Waals attraction. There have been many experimental 

measurements of the interaction force between various hydrophobic 

surfaces in aqueous solutions. These studies have found that the hydrophobic 

force between two macroscopic surfaces is of extraordinarily 

long range, decaying exponentially with a characteristic decay length of 

1–2 nm in the range 0–10 nm, and then more gradually further out, and 

this force can be much stronger than those predicted on the basis of van 

der Waals interaction, especially between hydrocarbon surfaces for which 

the Hamaker constant is quite small. 

It is now well established that a long-range (�10 nm) attractive force 

operates between hydrophobic surfaces immersed in water and aqueous 

solutions [136]. Unfortunately, so far, no generally accepted theory has 

been developed for these forces, but the hydrophobic force is thought to 

arise from overlapping solvation zones as two hydrophobic species come 

together [2]. In fact, Eriksson et al. [137] have used a square-gradient variational 

approach to show that the mean field theory of repulsive hydration 

forces can be modified to account for some aspects of hydrophobic 

attraction. Conversely, Ruckenstein and Churaev suggest a completely


different origin that attributes the attraction to the coalescence of vacuum 

gaps at the hydrophobic surfaces [138]. 

In recent years, a number of studies have been undertaken to study 

the effect of nanoscale bubbles found on hydrophobic surfaces to 

explain the hydrophobic forces reported in many surface force measurements. 

These bubbles may be present on the hydrophobic surfaces 

when first immersed in aqueous solutions, or may form from dissolved 

gases after immersion. Considine et al. [139], when undertaking measurements 

between two latex spheres, noted a large attractive force with 

a range much in excess of that expected from van der Waals attraction 

and independent of electrolyte concentration. They observed that degassing 

of solutions reduced the range of this attractive force significantly. 

Re-gassing of the solution restored the original range of this force, showing 

the influence of dissolved gas on the measurement of hydrophobic 

forces. Mahnke and colleagues [140] studied both the effect of dissolved 

gas and the degree of hydrophobicity of surfaces on the range of attractive 

forces. When surfaces were used that gave large (�25 nm) jump-in 

events, degassing of the intervening medium reduced the range of measurable 

attractive forces. For combinations of surfaces that gave short 

jump-in events, degassing of the solutions had little effect. It can be concluded 

that the long-range hydrophobic attraction can be accounted for 

by the presence of nanobubbles attached to the hydrophobic surfaces. 

The presence of such bubbles has been confirmed by the use of tapping 

mode AFM on hydrophobised silicon wafers [141, 142]. Bubble-like features 

observed on these surfaces show a high phase contrast with the 

rest of the surface, suggesting very different mechanical properties to 

the silicon surface. Force curves taken at the sites of these putative nanobubbles 

show much greater attractive and adhesive forces with a hydrophobic 

AFM probe than when taken from a bare area of the surface. 

Zhang and colleagues examined the effects of degassing and liquid temperature 

on the number and density on the surface of the nanobubbles 

[143]. Degassing of water and ethanol under vacuum reduced the surface 

density of nanobubbles to a very significant extent. Increasing the 

temperature of the fluid also increased the number and size of the nanobubbles 

on the surface, a phenomena witnessed by another group who 

also observed the spontaneous appearance of nanobubbles as the liquid 

temperature was increased [144]. For measurements where the hydrophobic 

force being measured is a result of the interaction of bubbles on 

the opposing surfaces, the forces measured are actually capillary forces 

rather than true hydrophobic forces, albeit capillary forces present as a 

result of the hydrophobicity of the surfaces. For those who wish to read 

further into the origins of forces measured between hydrophobic surfaces 

in aqueous solutions, the authors would like to draw attention to a number 

of reviews in the literature [145–147].


2.3.7 Effect of Hydrodynamic drag on AFM Force 

Measurements 

When performing measurements with particles in liquid, the effects of 

hydrodynamic drag on both the particle and also the cantilever may be significant, 

depending on the velocities at which measurements are taken. In 

particular, the effects of confinement of the liquid between two particles or 

between two surfaces are important. As the distance between the two surfaces 

decreases, the finite drainage time for the confined liquid produces a 

force dependent on the separation distance, the velocity of the approach as 

well as the viscosity and density of the fluid medium. Ignoring any contribution 

of drag on the cantilever to this effect, the hydrodynamic force, F H, 

for a sphere approaching a plane surface is given by a modified version of 

Stoke’s law for the drag force on a sphere [148, 149]: 

F � 6πν�r � 

H s c 

(2.58) 

where υ is the velocity of the probe, � is the dynamic viscosity of the 

surrounding fluid, r s is the radius of the spherical particle and � c is a correction 

applied to Stoke’s law to account for the presence of the confining 

wall in close proximity. 

where 

� c 

4 

� � sinh� 

3 

∞ 

∑ 

c c 

n�1 

n( n � 1) 

( 2n � 1)( 2n � 3) 

⎡ 2sinh( 2n � 1) �c 

+ ( 2n + 1) 

sinh2� 

⎤ 

⎢ 

c 

− 1⎥ 

⎢ 2 2 

⎣⎢ 

4sinh ( n � 0. 5) �c � ( 2n � 1) sinh2� 

⎥ 

c ⎦⎥ 

�1 

D � rs 

D r 

� cosh �ln 

rs 

rs 

⎛ 

⎧ 

⎞ 

⎪ 

⎪⎛ 

⎞ 

⎜ ⎨ 

⎪ ⎜ 

⎝⎜ 

⎠⎟ 

⎪ 

⎪⎝⎜ 

⎠⎟ 

⎩⎪ 

� s 

� 

⎡ 

⎢⎛D 

� r ⎞ 

⎜ s 

⎢⎜ 

⎢⎜⎝ 

rs 

⎠⎟ 

⎣ 

2 

⎤⎫⎪ 

⎥ 

⎪ 

� 1⎥ 

⎬ 

⎪ 

⎥⎪ 

⎦⎪ 

⎭⎪ 

(2.59) 

(2.60) 

where D is the distance between the plane surface and closest point of the 

sphere. For measurements where r � �h, then this can be simplified to: 

F 

H 

rs 

� 

D 

6πν� 

2 

(2.61) 

In most cases, contributions due to interactions between the surface 

and the cantilever itself can be neglected. However, depending on the 

size of the colloid probe and the speed at which the experiment is carried 

out, this may not always be the case. Vinogradova et al. [150] studied the

2.4 AdHESION FORCES MEASUREd By AFM 67 

effect of sphere size and probe speed on the contribution of drag on the 

AFM cantilever to measured hydrodynamic forces. They found that for 

the cantilever used that at speeds of 7.5 �m s �1 and for spheres of radii 

less than 3 �m, the cantilever did measurably contribute to the observed 

effects. Obviously, for faster speeds, the minimum sphere size to prevent 

cantilever contributions confounding sphere–plane measurements will 

increase. For most operating conditions, the authors recommended using 

colloid probes of no less than 5 �m in radius. 

2.4 AdHESIon FoRCES MEASuREd by AFM 

Adhesive forces measured as the pull-off force in AFM measurements 

represent the sum of all the interaction forces occurring in the contact 

regime. This includes long-range forces such as van der Waals and electrostatic 

forces; capillary forces (if measurements are undertaken in air); 

solvation forces; hydrophobic interactions and steric interactions as well 

as any chemical bonding between groups present on the surfaces. 

2.4.1 Contact Mechanics and Adhesion 

The magnitude of the adhesion between two surfaces is dependent 

upon the contact area at the junction between the surfaces as well as 

the interaction forces themselves. The contact area will depend upon 

the mechanical deformation of the materials due to the applied force 

and material properties. The understanding of the relationship between 

adhesive forces and contact mechanics as generally applied in the field of 

force microscopy is dependent upon the works of Johnson, Kendal and 

Roberts (JKR theory) [151] and Derjaguin, Muller and Toporov (DMT 

theory) [152] some decades ago. According to the JKR model of contact 

mechanics, for a sphere–plane system, the adhesion (pull-off) force can 

be related to the work of adhesion, contact area and mechanical compliance 

of the interacting surfaces by: 

JKR 3 

ac 

2 

FAd � πRpWa 

� 

2 

R 3 

2 

p 

6πW 

E* 

a 

(2.62) 

where R p is the radius of the probe sphere, W a is the work of adhesion per 

unit area and a c is the contact radius. The parameter a 2 c/R is the sample 

deformation and �. E* is the reduced Young’s modulus for the system: 

2 

1 3 1 1 

s 

E* 4 Es E f 

� 

⎛ 

⎜ � ν � ν 

⎜ � 

⎜ 

⎝⎜ 

2 

f 

⎞ 

⎠⎟ 

(2.63)


where E s, E f and v s, v f are the Young’s modulus and Poisson ratios for the 

sphere and flat surface respectively. The JKR model applies well for large 

probes with soft samples and large adhesions. For the case of relatively 

small tips with surfaces with high Young’s moduli and low adhesion, the 

DMT model may apply better. For the DMT theory, a slightly different 

relationship is found: 

a F R W 

FAd R W 

R R E 

DMT 

c 

p a 

� p a � 

p 

� 

2 ( 2π 

) 

2π 

3 2 

* 

p 

2 

3 

(2.64) 

The JKR and DMT models are really descriptions of the two ends of a 

continuum. Tabor suggested a way of deciding which of these two models 

would be the best to apply to a certain situation. From the following 

relationship, if the factor � R is greater than unity, then the JKR theory 

would be best applied, with DMT being appropriate for � R values less 

than unity [153, 154]: 

� R 

2 

a p 

0 3 

1 

⎞ 3 

* ⎟ 

⎛ 

⎜W 

R 

� 2. 92 ⎜ 

⎝⎜ 

E z ⎠ 

(2.65) 

where � R is effectively the ratio of the elastic deformation due to the applied 

load and adhesion to the effective range of the surface forces (z 0) [153, 155]. 

For intermediate systems where values of � R are close to unity, then a treatment 

using the Maugis–Dugdale theory is more appropriate [155]. 

The AFM has been used to measure adhesive forces between particles 

and process surfaces. One important example is adhesion between particles, 

including both inorganic colloidal particles and bacterial cells, and 

filtration membranes. This interaction is of great importance when considering 

the fouling and biofouling of such surfaces. Particles adhere to 

the process membranes and reduce flow through the membrane, greatly 

reducing filtration, the efficiency and working lifetime of the membranes. 

The process testing of new membranes is potentially expensive and time 

consuming. The quantification of adhesion forces between colloids and 

membranes can provide an important contribution to developing the 

theoretical prediction and optimisation and control of many engineering 

separation processes. As a result, the development of AFM methods to 

quantify the adhesion of different materials to membranes of different 

compositions can potentially be very useful for membrane manufacturers 

and engineers [156]. When particle sizes are greater than the pore size 

in the absence of repulsive double layer interactions, such particles may 

plug the pores very effectively, leading to a catastrophic loss in filtration 

flux. Of the many established membrane characterisation techniques,

2.4 AdHESION FORCES MEASUREd By AFM 69 

only the colloid probe method can measure the adhesive forces between 

particles and membrane surfaces and hence allow prediction of the membrane 

fouling properties of the particles. In addition, the ability to make 

measurements in liquid allows the matching of observation conditions to 

those that occur in practice. 

Studies have also been carried out on the adhesion forces between 

calcium carbonate crystals and stainless steel surfaces. The adhesion of 

CaCO 3 to steel process equipment surfaces plays an important role in the 

formation of scale deposits in desalination plant equipment, as well as in 

domestic appliances such as kettles and other household appliances. Al- 

Anezi et al. [157] measured the adhesion between CaCO 3 probes and stainless 

steel surfaces of different grades of roughness. In Figure 2.7 is an SEM 

image showing an example of a CaCO 3 crystal mounted on an AFM cantilever. 

The roughest surface had the lowest adhesion than the two smoother 

surfaces examined. The effect of liquid environment was also examined. 

Adhesive forces measured in sea water to which 2 ppm of an anti-scaling 

agent had been added were significantly more reduced than when measured 

in sea water alone. In addition, the proportion of measured force 

curves that showed no observable adhesion rose from 1% of all obtained 

force curves in sea water to 57% with the addition of the anti-scale agent. 

FIGuRE 2.7 SEM image of a CaCO 3 crystal mounted upon an AFM cantilever for use in 

determining adhesion with stainless steel surfaces.


2.5 EFFECt oF RouGHnESS on MEASuREd AdHESIon 

And SuRFACE FoRCES 

The continuum theories outlined above, such as the JKR and DMT 

theories, assume that perfectly smooth surfaces come into contact [2]. 

Unfortunately, the degree of roughness of particles and surfaces is quite 

variable, and often, except for when studying molecularly smooth surfaces, 

some account may be needed to be taken of roughness. The presence 

of asperities on surfaces coming into contact serves, in most cases, 

to effectively decrease the contact area. There are a number of models 

that have been developed to account for the effect of surface roughness 

on measured adhesion when trying to infer various properties of interactions 

from adhesion forces. These generally use some measure of roughness, 

such as the root mean square (rms) roughness of the surface, or 

values for mean asperity size to account for the reduced contact areas 

due to the presence of surface asperities [158–165]. As well as serving 

to keep the two surfaces separated, the angle at which asperities on the 

particle surfaces approach each other may also affect the effective contact 

area and thus the measured adhesion [166]. Rabinovich et al. [162] determined 

that surface roughness values as small as 1.6 nm rms were significant 

and could reduce adhesion values by as much as fivefold from that 

expected. 

In addition, rough particles make determination of the radius of probe 

particles, and hence normalisation by particle size, difficult. Larson and 

colleagues [167] determined an effective probe radius when performing 

measurements between TiO 2 colloids and crystal surfaces by fitting force 

data to an electrical double layer model, with surface potential values 

determined independently. This allowed calculation of an effective probe 

radius that was used to normalise all subsequent force measurements. 

AbbREVIAtIonS And SyMbolS 

a Effective hard sphere particle radius in solution m 

ac Contact radius m 

ai Particle radius of molecule i M 

a VW van der Waals gas constant N m 4 mol �2 

A131 Effective Hamaker constant in medium 3 J 

AH Hamaker constant (in vacuum or in medium) J 

bVW van der Waals gas constant m3 mol�1 c Velocity of light in a vacuum (2.998 � 108 ) m s�1

C Capacitance C V �1 

C D Debye interaction constant J m 6 

C K Keesom interaction constant J m 6 

C L London interaction constant J m 6 

C T Interaction constant J m 6 

C UV Cauchy Plot parameter � 

d Distance to OHP (surface of shear) m 

D Surface to surface separation distance m 

D jtc Jump-in distance m 

D 0 Characteristic decay length m 

e Elementary charge (1.602 � 10 �19 ) C 

E* Reduced Young’s modulus Pa s �2 

E s Young’s modulus for the sphere Pa 

E f Young’s modulus for the flat surface Pa 

f 0 Force extrapolated to separation distance, D � 0 N 

F Force between surfaces/particles N 

JKR 

FAd DMT 

FAd ABBREvIATIONS ANd SyMBOLS 71 

Adhesion pull-off force (JKR model) N 

Adhesion pull-off force (DMT model) N 

FH Hydrodynamic force for a sphere approaching a 

plane surface 

N 

FR Repulsive interparticle force N 

FSOL Hydration force N 

h Planck’s constant (6.626 � 10 �34 ) m 2 kg s �1 

¯h Planck’s constant divided by 2� (6.626 � 

10�34 /2�) 

J s rad�1 k Boltzmann constant (1.380 � 10�23 ) J K�1 kc Spring constant of the cantilever N m�1 keff Effective spring constant of the cantileversample 

system 

N m�1 ks Stiffness of the sample N m�1 K Constant in force equation N 

Ki Equilibrium constant for ionisation reaction i M 

l Correlation length of the orientational ordering 

of water molecules 

m 

n Number of gas molecules mol


n o Ion number concentration in bulk m �3 

n oi 

Refractive index of component i � 

p Pressure N m �2 

Q Charge on plates C 

r Interparticle separation (centre to centre) m 

r s Radius of the spherical particle m 

R Gas constant J mol �1 K �1 

R i Radius of sphere i m 

R p Radius of the probe sphere m 

R t Radius of curvature of the probe tip m 

S � Surface area of spherical shell m 

T Absolute temperature K 

u i Dipole moment of molecule or atom i C m 

v Velocity of the probe m s �1 

v f Poisson ratios for a flat surface � 

v i Orbiting frequency of electron i s �1 

v s Poisson ratio for a sphere � 

V Volume of container m 3 

V A Attractive interaction energy J 

V R Repulsive interaction energy J 

V T Total interaction energy J 

�V Voltage difference V 

w (r) Interaction potential J 

W(D) Interaction energy per unit area as a function of 

distance 

J m�2 Wa Work of adhesion between two bodies J 

xjtc Cantilever deflection due to the jump-in m 

X ˆ 

COO Fraction of carboxyl groups ionised � 

zi Valence � 

z0 Effective range of the surface forces m 

Z� Charge number due to negative groups on the 

BSA surface 

� 

Z� Charge number due to positive groups on the 

BSA surface 

� 

ZAB Charge number from acid–base equilibria �

GREEk SyMBOLS 73 

Z cl � Number of bound chloride ions � 

Z COO ˆ Charge number due to ionisation of carboxyl 

groups 

Z T Total charge number of BSA molecule � 

GREEk SyMbolS 

� Hydrodynamic radius (� a � d) m 

� 0i Electronic polarisability of molecule i m 3 

� Activity coefficient of chloride ion in NaCl solution � 

� i Reduced surface potential i � 

� ik Interfacial energy between components i and k J m �2 

ε 0 Permittivity of vacuum (8.854 � 10) C V �1 m �1 

ε ri Dielectric constant of component i � 

� Zeta potential V 

�i Number of atoms per unit volume of the interacting 

material 

m�3 � Distance parameter in Lennard-Jones equation m 

�d Charge density of diffuse double layer C m�2 �m Molecular diameter m 

�o Surface charge density C m�2 � Debye–Hückel parameter m�1 � Characteristic wavelength m 

�c Correction applied to Stoke’s law � 

� Viscosity of fluid N s m�2 �R Ratio of the elastic deformation to the applied load and 

adhesion to the effective range of the surface forces 

� Electrostatic potential V 

�� Electrostatic potential at outer cell boundary V 

�d Electrostatic potential at OHP (� zeta potential) V 

�o Electrostatic potential at particle surface V 

wi Characteristic frequency of electromagnetic radiation rad s�1 wUV UV characteristic frequency of electromagnetic 

radiation 

rad s�1 ε Depth of the potential energy well J 

�


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C H A P T E R 

3 

Quantification of 

Particle–Bubble 

Interactions Using Atomic 

Force Microscopy 

Nidal Hilal and Daniel Johnson 

O U T L I N E 


3.2 Particle–Bubble Interactions 82 

3.3 Determination of Particle–Bubble Separation 86 

3.4 Determination of Contact Angle from Force–Distance Curves 88 

3.5 Effect of Surface Preparation on Particle–Bubble Interactions 91 

3.5.1 Effect of Particle Surface Chemistry on Particle–Bubble Interactions 91 

3.5.2 Effect of Surfactant on Particle–Bubble Interactions 94 

3.6 Effect of Loading Force on Particle–Bubble Interactions 97 

3.7 Effect of Hydrodynamics on Particle–Bubble Interactions 98 

3.8 Conclusions 100 

List of Abbreviations 101 

List of Symbols 101 

References 102 



82 3. QUANTIFICATION OF PARTICLE–BUBBLE INTERACTIONs 

3.1 IntroDuCtIon 

The attachment of particles to bubbles in solution is of fundamental 

importance to several industrial processes most notably in froth flotation. 

Froth flotation is a significant industrial process, used primarily in the 

separation of mineral particles and also in the treatment of wastewater. 

The process of flotation involves the suspension of finely ground mineral 

particles in a chamber through which large volumes of air or another 

gas are bubbled. Hydrophobic particles will attach more readily to air 

bubbles passing through the medium and will thus rise to the top of 

the chamber where they form froth at the surface and become separated 

from other materials. Hydrophilic particles, which are less able to attach 

to the air bubbles, will eventually sink to the bottom of the chamber. In 

addition, a number of additives, including surfactants, termed collectors, 

may also be introduced to increase the hydrophobicity of the particles of 

interest and consequently increase the efficiency or specificity of the flotation 

process [1, 2]. 

It follows that an understanding of the nature and strength of the interactions 

between colloidal particles suspended in solution and air bubbles 

is of fundamental importance to developing new ways of increasing flotation 

efficiency and modulating specificity. Atomic force microscopy 

is one technique which is able to quantitatively measure interactions 

between single particles and interfacial boundaries. Over the past decade 

the atomic force microscope (AFM) has been adapted for use in studying 

the forces involved in the attachment of single particles to bubbles in 

the laboratory. This allows the measurement of actual Derjaguin, Landau, 

Vervey and Overbeek (DLVO) forces and hydrodynamic, hydrophobic 

and adhesive contacts to be measured under different conditions. In 

addition, contact angles may be calculated from features of force versus 

distance curves. The purpose of this chapter is to illustrate how the AFM 

and particularly the colloid probe technique can be used to make measurements 

of single particle–bubble interactions and to summarise the 

current literature describing such experiments. 

3.2 PArtICLE–BuBBLE IntErACtIonS 

During collisions between mineral particles and air bubbles in flotation 

cells, attachment is determined by the thinning of a film of water in the 

intervening space. This consists of a layer of bulk water and a hydration 

layer which surround both the particle and the bubble (see Figure 3.1). On 

initial approach, the bulk fluid layer will become displaced [3]. However, 

the time required for this bulk layer to drain from the confined space

Bubble 

3.2 PARTICLE–BUBBLE INTERACTIONs 83 

Hydration 

layers 

between the particle and the bubble will add a hydrodynamic component 

to the attachment kinetics. In flotation, if the time required for this film to 

rupture (the induction time) is less than the actual contact time, then the 

particle will be unable to attach to the bubble [4]. Further approach will 

cause the hydration layers to become thinner and less stable. As this layer 

becomes destabilised, the particle and bubble will be allowed to attach 

directly, leading to the formation of a three phase contact (TPC) line. The 

more hydrophobic the particle surface, the thinner and less stable any 

hydration layer will be. Consequently, the more hydrophobic in character 

a particle is, the more readily it will attach to air bubbles in solution. This 

is the mechanism by which the flotation of fine particles is achieved [1, 2]. 

Derjaguin and Dukhin [5] explain that the main thermodynamic parameter 

involved in the particle–bubble interaction is the disjoining pressure, 

which is defined by them as the derivative of the free energy with respect 

to the thickness h of this wetting layer per unit area. This disjoining pressure 

is formed by a combination of pressures: 

P � N � A � S 

( h) ( h) ( h) ( h) 

Particle 

Bulk fluid 

layer 

FIGurE 3.1 Simple illustration of a basic particle–bubble interaction. On approach 

there are three fluid layers present between the particle and the bubble. These are hydration 

layers on both the particle and the bubble (represented by the dashed line) and a layer 

of bulk fluid in the middle. The confinement and drainage of this bulk fluid layer leads to a 

hydrodynamic component to the interactions. 

(3.1) 

where P is the disjoining pressure, N the ionic double layer repulsion 

per unit area, A the contribution due to van der Waals interactions per 

unit area and S (h) the contribution of particle surface hydrophobicity to 

the disjoining pressure. S (h) will tend towards zero for very hydrophobic 

surfaces. 

As described by Sutherland [6, 7], the probability of a particle being 

collected during flotation (P) is a composite of the probability of particle– 

bubble collision (P c), the probability of such a collision leading to adhesion


(P a) and the probability that a particle–bubble aggregate will become 

detached (P d): 

P � P P ( 1 � P ) 

c a d 

(3.2) 

When conducting a bubble–particle interaction measurement using an 

AFM or similar piece of equipment, the probability of collision is determined 

by the user, and as such will not be considered further here. In 

terms of kinetics the attachment of a particle to the bubble depends upon 

the overcoming of an energy barrier by the kinetic energy imparted during 

the collision [6, 8]: 

⎛ E ⎞ 

1 

Pa 

� exp ⎜ 

⎜� 

⎝⎜ 

E ⎠⎟ 

k 

(3.3) 

where E 1 is the energy barrier for adhesion and E k the kinetic energy of the 

collision. The energy barrier is a result of the interaction of the repulsive 

and attractive forces acting between the particle and the bubble. The sum of 

forces between the particle and bubble can be summarised as follows: 

F � Fd � Fe � Fh 

(3.4) 

where F d and F e are the London dispersion van der Waals force and the 

electrical double layer force, respectively, representing traditional DLVO 

theory forces; and F h the hydrophobic attractive force between the particle 

and the bubble. When conducting AFM measurements between 

colloidal particles and a bubble, these forces may be manifested in the 

approach part of the force–distance curve. Models which describe longrange 

forces may be fitted to force–distance data to investigate the nature 

of the interaction under observation. 

Finally, the probability of detachment can be described by the following 

relationship [8]: 

P 

d 

Wa E 

� � 

E 

� ⎛ ⎞ 

1 

exp ⎜ ’ 

⎝⎜ 

⎠⎟ 

k 

(3.5) 

Here E k ’ is the kinetic energy of detachment and is not to be confused 

with E k the kinetic energy of collision; W a the work of adhesion. This latter 

quantity W a is of interest when carrying out AFM experiments as it 

can be directly related to adhesion measurements carried out. According 

to Johnson–Kendall–Roberts (JKR) theory, this is related to adhesion by 

the following association [9]: 

F 

ad 

RW 

� 3π 

2 

a 

(3.6)

3.2 PARTICLE–BUBBLE INTERACTIONs 85 

where F ad is the measured adhesion force and R the particle radius of 

curvature. This relationship assumes an idealised geometry of a sphere 

approaching a flat surface. If the air bubble is much greater in size than 

the particle, then this approximation is valid. However, it should also 

be noted that in practice the particles present during flotation are most 

likely to be irregular in shape, far removed from the idealised sphere. 

The first reported use of the AFM to measure interaction forces between 

colloidal particles and air bubbles in a fluid environment was by Butt 

[10], who measured the interaction between glass beads and an air bubble 

in water and between glass beads and water droplets in air. This was 

shortly followed by another study carried out by Ducker et al. [11]. In the 

work of Butt, air bubbles were immobilised onto the bottom of a polytetrafluoroethylene 

(PTFE) cuvette. It was concluded that hydrophilic particles 

approaching air bubbles experienced repulsive forces on approach. 

Conversely hydrophobic particles snapped in to the bubbles upon making 

close approach, becoming trapped within the air–water interface. 

In other studies reported in the literature, various immobilisation strategies 

have been used including highly ordered pyrolytic graphite (HOPG) 

surfaces [12]. When a hydrophobic substrate is used, such as HOPG, in 

an aqueous environment, the bubble will try to minimise its area of contact 

with the water by attaching itself to the substrate. As a result hydrophobic 

substrates are more suitable surfaces to attach the bubbles to than 

hydrophilic surfaces. Ducker et al. [11] used a slightly more sophisticated 

approach. Here a thin layer of mica with a small perforation was placed 

over a HOPG substrate. The bubble was then placed over the hole. This 

served to clamp the bubble in place, minimising any potential lateral 

movement of the bubble during measurement acquisition. Other immobilisation 

strategies involve attaching the bubble to a scratch made on the 

inside surface of a Petri dish [13] and attaching the bubbles to hydrophobic 

squares created by functionalising a surface with octanethiol [14]. 

Producing air bubbles of an appropriate size using a small micro-syringe 

or micro-pipette and laboratory air is a relatively simple operation. To create 

a bubble of 250-�m diameter would require approximately 0.033 �l of air, 

assuming the bubble was hemispherical in shape. Creating bubbles of a size 

much smaller than this size becomes problematic. As the size of the bubble 

decreases, the Laplace pressure (the pressure difference between that inside 

the bubble and that outside the bubble) will increase. This makes small 

bubbles unstable and short lived as this high pressure will increase their 

tendency to dissolve in the surrounding fluid. However, there have recently 

been reports of very small nano-scale bubbles existing on hydrophobic 

interfaces under the right conditions [15–18]. It has been suggested that 

these nano-bubbles are responsible for the hydrophobic attraction observed 

between hydrophobic surfaces [15, 16, 19]. Jump-in between hydrophobic 

surfaces would thus be expected to occur when nano-bubbles attached to 

opposite hydrophobic surfaces come into contact.


3.3 DEtErmInAtIon oF PArtICLE–BuBBLE 

SEPArAtIon 

One of the main uncertainties involved when making single particle 

bubble measurements is the determination of the separation distance 

between the probe and the air–liquid interface. With a contact between 

hard surfaces, there is normally a clear transition as contact is made, but 

for deformable surfaces this is not necessarily obvious. First, deformation 

of the bubble by both long-range interaction forces prior to contact and 

compression by the probe after contact needs to be taken into account 

(Figure 3.2). When a hydrophilic particle comes into contact with a bubble, 

a thin wetting film may separate the particle from the bubble. As the 

particle encounters this wetting film at small separations, the air–liquid 

interface will become deformed due to hydrodynamic factors, producing 

an apparent repulsion [20]. A hydrophobic particle may sit partially 

inside the bubble to a distance dependent upon their contact angle, or 

may be completely engulfed within the bubble. Together, these factors 

make an exact determination of the separation distance and attachment 

point more problematic than when considering interactions between 

hard solid surfaces. 

In the early paper by Ducker et al. [11], it was assumed that the bubble 

was deformed in a linear manner, resembling a Hookean spring. As such 

d 0 d n 

FIGurE 3.2 On approach of a particle into the vicinity of the bubble, long-range interactions 

will result in deformation of the bubble prior to contact. The nominal distance (d n) is the 

distance that would exist between the particle and the bubble if deformation did not occur. 

The actual distance (d 0) differs from d n by the size of the deformation. The size of the particle 

here is important as the magnitude of interaction forces will scale with its radius (R p), if the 

particle is a sphere. Note that in the illustration here the bubble is deforming as from a net 

repulsive interaction. With a net attraction deformation will be towards the particle. 

R p

3.3 DETERMINATION OF PARTICLE–BUBBLE sEPARATION 87 

the stiffness of the total system will behave as for any two linear springs 

in series: 

1 1 1 

� � 

ktot kc kbubble 

(3.7) 

where k b, k c and k tot are, respectively, the spring constants of the bubble, 

the cantilever and the bubble and lever combined. This means that the 

probe pressing against the bubble would lead to a gradient in the contact 

region based on both the deflection of the lever and the ‘stiffness’ of the 

bubble. The contact slope should thus be [21]: 

∆x 

k 

� 

∆z 

k � k 

bubble 

c tot 

(3.8) 

where �x and �z are the changes in cantilever deflection and piezotranslation 

distance, respectively. It is also assumed that the particle 

approaches in a direction perpendicular to the interface. If this is not the 

case, then the interaction becomes somewhat more complex due to the 

potential slippage of the particle along the interface. 

Attard and Miklavic [21, 22] in a thorough theoretical treatment of 

bubble deformation concluded that for small deformations relative to 

the bubble radius, air bubbles behave like linear Hookean springs, with 

the deformation given by equation (1.1) in Chapter 1. Unlike with solids, 

where the material properties determine stiffness, it is the interfacial 

tension and the pressure drop across the interface which determine the 

stiffness of the bubble. The same behaviour is also displayed by liquid 

droplets. Interestingly, when a micro-manipulation rig was used to apply 

large deformations (i.e. the deformation was �30% of the bubble diameter) 

to air bubbles in aqueous solutions, they were found to have a pseudoelastic 

behaviour [23]. However, deformation induced during AFM-based 

measurements is orders of magnitude smaller than this. Currently it is 

uncertain as to how large a deformation needs to occur to move from a 

linear, Hookean, deformation to a pseudo-elastic deformation. 

To calculate the separation distance, this linear deformation needs to 

be taken into account. From the slope and intercept of the contact part of 

the force curve, this can be estimated [12]: 

x 

d � �z � d 

� � 

c 

� 

c 

c 

(3.9) 

where � c is the slope of the contact region on the force curve (� c � �x/�z) 

and c the intercept; d c the particle–bubble distance when in ‘contact’, 

i.e. the thickness of any wetting film, etc. or the depth to which the interface


has been penetrated. This still leaves the need to either obtain the thickness 

of the wetting film from another source or assume that it is too thin to 

be significant, which may not be the case, particularly for very hydrophilic 

particles. 

Perhaps the simplest method for finding the zero contact point is to use 

the point at which the probe snaps-in during a jump to contact as suggested 

by Butt [9]. In cases where there are only repulsive forces evident prior to 

contact, there will be no snap-in and this method cannot be used. However, 

in cases where estimates of particle contact angle are to be made from force 

curves, this approach can be very useful. An interesting approach has been 

described by Gillies et al. [24]. At large separations, interaction forces are 

very weak, and thus the bubble or droplet will behave as though it is rigid 

at such separations. The force versus distance data can be shifted along 

the distance axis to coincide with the linear Poisson–Boltzmann theory for 

rigid bodies. However, this technique requires determination of the surface 

potentials from some other source, such as by electrophoresis, making its 

implementation problematic in laboratories where the appropriate equipment 

is not available. 

3.4 DEtErmInAtIon oF ContACt AnGLE From 

ForCE–DIStAnCE CurvES 

As mentioned previously, the attachment of particles to air bubbles in 

an aqueous environment is largely mediated by the degree of hydrophobicity 

of the particle. A hydrophobic particle will prefer to be in contact 

with the bubble, minimising its contact with surrounding water, whereas 

a hydrophilic particle will retain a thin wetting film. One conventional 

method of measuring the wettability, and hence the degree of hydrophobicity 

of a surface is to measure the contact angle of a drop of water on 

that surface, which is the angle formed by the TPC line [25–27]. When 

the particle comes into contact with an air bubble, the TPC formed will 

likewise also contain a contact angle. 

Figure 3.3 shows a basic schematic representation for the particle– 

bubble interaction. The particle has penetrated the bubble to a distance D. 

The angle � represents the immersion angle of the particle, which gives 

an indication of the position of the TPC line with regard to the particle. 

The contact angle is indicated by � and corresponds to the angle of contact 

internal to the droplet during conventional contact angle measurements. 

The contact angle is related to the interfacial tensions of the three 

interfaces present around the TPC by the Young equation: 

� � � 

cos� � 

� 

SV SL 

LV 

(3.10)

3.4 DETERMINATION OF CONTACT ANgLE FROM FORCE–DIsTANCE CURvEs 89 

θ 

FIGurE 3.3 A particle in direct contact with a bubble with a net force of zero, at which 

point it is immersed to a distance D. When no net force is present then the immersion angle 

� is equal to the contact angle �. The contact angle may be receding or advancing depending 

upon the direction of travel of the particle. 

where � indicates interfacial tension, with the subscripts SV, SL and LV 

denoting the solid–vapour, solid–liquid and liquid–vapour interactions, 

respectively. 

In addition, the tension around the TPC line, called the line tension, 

may need to be taken into account. For macro-scale experiments, the line 

tension is negligible and is usually ignored, with the Young equation 

being a good approximation. However, at small length scales, the line 

tension becomes more significant and further terms need to be added. 

For a spherical particle in an interface, the contact angle will be [28, 29]: 

� � � 

cos� � 

�� 

SL SV 

LV 

(3.11) 

where � is the line tension and � the geodesic curvature of the TPC line. 

As the TPC line is circular, then: 

� 

� 

� 

1 r sin 

(3.12) 

where r is the radius of the circle drawn out by the TPC line (equal to the 

radius of the particle when immersed halfway). 

In many systems, there exists a contact angle hysteresis between an 

advancing (� a) and a receding contact angle (� r), i.e. a different contact angle 

may be measured depending upon whether the TPC line is advancing or 

receding over a particle surface. The reason for this hysteresis is generally 

ascribed to roughness and heterogeneity of the surface chemistry, although 

other factors may be of importance, such as the existence of a contaminant 

layer or polymer coatings, etc. [30–35]. 

As the particle enters into the bubble, the TPC line is receding across the 

particle surface. As a result it is the receding contact angle which may be calculated 

from the approach part of the force curve, and the advancing contact 

α 

D


angle when the particle is being extricated from the bubble. The jump- 

in force is dominated by capillary forces, at least in the case of a particle with 

a hydrophobic enough surface to be able to form a TPC line. As such, the 

capillary force may be related directly to � r, as illustrated by equation (3.15) 

[36–38]: 

F � 2πR� sin� sin( � � �) 

CAP r 

(3.13) 

where � represents the interfacial tension. When the net forces are zero 

(i.e. F CAP � 0), � r will be equal to �; when this occurs, equation (1.14) may 

be used to calculate � r [36, 39]: 

cos 

� r 

( R Dr 

) 

� 

R 

� 

(3.14) 

Here the penetration depth D r can be extracted from force curves by 

taking the distance from the initial jump-to-contact to the point at which 

the force is zero, i.e. there is no net force acting on the cantilever. This is 

illustrated in Figure 3.4. When the particle is withdrawn from the bubble, 

the TPC line is advancing across the particle, hence contact angles determined 

are called the advancing contact angle (� a). If adhesion occurs, 

D a 

Dr 

FIGurE 3.4 A force curve, showing the relevant measurements to obtain D r and D a. D r 

is found by measuring the distance from jump-in to the point at which a net force of zero, 

equivalent in size to the free level force, is reached. From this distance on the approach 

curve, the receding contact angle � r is obtained. From a similar measurement on the retract 

curve (D a) the advancing contact angle � a may be obtained.

3.5 EFFECT OF sURFACE PREPARATION ON PARTICLE–BUBBLE INTERACTIONs 91 

then the advancing contact angle � a may be obtained from the retract 

part of the force trace. Here the adhesion force F AD can be related to the 

advancing contact angle: 

2 

a 

2 � 

FAD � 2πR� 

sin 

2 

(3.15) 

Other methods have been developed to measure contact angles using 

the AFM in tapping mode. Pompe et al. [40] scanned liquid drops on surfaces. 

By then using a cross section of the topography, they measured the 

contact angle and three-phase line tension parameters for the liquid drops. 

3.5 EFFECt oF SurFACE PrEPArAtIon on 

PArtICLE–BuBBLE IntErACtIonS 

3.5.1 Effect of Particle Surface Chemistry on Particle–Bubble 

Interactions 

As would be expected, the surface chemistry of the colloid probes has 

an important effect on their attachment to bubbles in aqueous solutions. 

In the literature there have been a number of studies in which the effect 

of the surface chemistry of various probes has been investigated for their 

importance in particle attachment to bubbles. 

In the first set of AFM-based experiments to measure particle–bubble 

interactions in the literature, as described by Butt [10], untreated hydrophilic 

glass particles were allowed to interact with air bubbles in aqueous 

media. When the glass approached the surface, a linear repulsive force 

was measured on contact, with no jump-in prior to contact. This was 

echoed in the work by Fielden et al. using hydrophilic silica particles [37], 

who also noted a linear repulsion with no jump-in. This is hardly surprising 

as both silica and glass have a tendency to carry a negative charge in 

water due to Si–OH groups on the surface [41], and the air–water interface 

of air bubbles also tends to be negatively charged for the majority of 

pH values, as evidenced by �-potential measurements [42, 43], leading to 

repulsive electrical double layer forces. In addition it would be expected 

that van der Waals forces between silica and air in water would also be 

repulsive, due to a negative Hamaker constant for the interaction of silica 

and air across water [26, 44]. This means that the DLVO forces in general 

will all tend towards repulsion in this case. 

Interestingly, a different result was reported by Ducker et al. [11] when 

interacting a silica sphere with an air bubble in water. Jump-in events 

were observed prior to contact, at a distance of 50 nm, before being followed 

by a linear repulsion after contact was made. It was speculated by 

the authors that at small separations, the air–water interface may change


sign under the influence of the approaching silica particle. A similar argument 

was used to explain the adhesion forces observed (�4 mN m �1 ), 

measured during retraction of the hydrophilic silica particles by Fielden 

et al. It has been noted elsewhere that if there is a sufficient difference 

in the magnitude of the surface potentials of two approaching bodies, 

then even if the bodies have potentials of the same sign at sufficiently 

small separations, an attractive force may occur [45]. It is worth bearing 

in mind that due to the very small surface areas of the interactions, these 

types of experiments are very sensitive to any contamination, even if great 

care is taken to prevent this. Deviations from the expected behaviour 

could easily be caused as a result of such contamination. In the literature, 

papers describing colloid probe-based particle–bubble interactions 

describe stringent techniques to minimise the risk of contamination. The 

potential problems due to probe contamination are a serious concern for 

all SPM techniques. See Chapter 1 for more information on this subject. 

Glass particles used by Butt et al. [10] were made hydrophobic by 

silanizing them in an atmosphere of dichloromethane. When these particles 

were allowed to approach an air bubble, their behaviour was found to 

have altered from that of hydrophilic particles. This time jump-in events 

occurred on approach to the bubble surface with no repulsive interaction 

prior to contact. When the particle was retracted large adhesion occurred, 

with the cantilever deflecting by a greater amount than could be detected 

by the instrument being used [10]. In the study by Fielden et al. [37] the 

silica particles were hydrophobized by either reacting with octadecyltrichlorosilane, 

or by dehydroxylation to create a surface with a more moderate 

degree of hydrophobicity. For the two types of hydrophobic surface, 

interactions between the particles and the bubbles were attractive at small 

separation distances. Furthermore, the attraction was dependent upon 

the degree of hydrophobicity of the surface. Frequently the particle was 

engulfed by the air bubble and much larger adhesion forces were measured 

than with the hydrophilic particle. It was concluded that the jumpin 

events observed were a result of hydrophobic attraction. These two 

studies illustrate the importance of hydrophobicity in particle–bubble 

attachment and for the degree of stability of particle–bubble aggregates. 

Preuss and Butt [39] measured the interactions of bubbles with silica 

particles coated with different surface concentrations of alkyl-thiol 

molecules and the resultant receding contact angles both with the colloid 

probe technique and by conventional means. They noticed that as 

well as more hydrophilic particles having shorter jump-in distances 

and less adhesion than hydrophobic particles, both the � r and adhesion 

forces increased as the mole fraction of alkyl-thiols was increased. 

As an increase in contact angle is conventionally related to an increase 

in hydrophobicity of a surface [27], the relationship between hydrophobicity 

and the stability of particle bubble attachment is again reiterated.


In addition the authors compared the contact angles obtained from the 

AFM measurements with those obtained conventionally on flat surfaces. 

It was found that the � r values obtained by the two methods differed, 

depending upon the contact angles measured. At low contact angles (i.e. 

more hydrophilic surfaces), contact angles measured with the colloid 

probe were higher than those measured on planar surfaces. At contact 

angles �60° the values obtained with the colloid probes were lower than 

those measured on flat surfaces, with measurements at intermediate contact 

angles in close agreement. These differences were explained by the 

authors as being possibly due to the differences in line tension between 

the different experimental set-ups [39]. 

The interactions of ZnS spheres with air bubbles at a range of solution 

pH values was examined by Gillies et al. [46, 47]. On approach, repulsion 

between the spheres and the bubbles was observed due to DLVO forces (the 

micro-spheres have a negatively charged surface in solution under the conditions 

of the experiments) and confinement of hydration layers, prior to a 

jump-in event. The magnitude of the repulsive force prior to jump-in was 

found not to vary upon alteration of solution pH to a significant effect at 

pH values of 8.5 or less. On increasing the pH above this level, the repulsion 

was increased by an order of magnitude, due to a much greater concentration 

of negative charges on the micro-sphere surface. Contact angles measured 

at the same time appeared to alter, based upon the number of times 

the micro-sphere had previously interacted with the bubble surface, leading 

to speculation that the ZnS surface was changing, either by being cleaned 

or coated by the interaction. In addition a slight increase in the receding 

contact angle was observed concomitant with a rise in pH. Leaving the 

micro-spheres in zinc solutions for extended periods of time caused the 

particle surface to change from a predominantly zinc hydroxide to a predominantly 

zinc oxide surface, resulting in a greater degree of hydrophobicity. 

This resulted in contact angles measured in these aged micro-spheres 

which were approximately 10° greater than those of the none-aged spheres. 

Wangsa-Wirawan et al. [13] measured the adhesion forces due to the 

interactions between protein inclusion bodies and air bubbles. Both pH 

and ionic strength of the surrounding solution was altered and the effects 

measured. A maxima in the adhesion forces was reached at pH 5, with a 

decrease at higher pH values, although adhesion was still observed. The 

inclusion bodies were expected to carry a net overall negative charge at 

pH values �5, leading to electrostatic repulsion between the bodies and 

the negatively charged air–water interface. It was concluded that whilst 

the electrostatic forces modulated the adhesion, hydrophobic interactions 

between the inclusion bodies and the air–bubble played a more dominant 

role in the adhesion. Additionally it was reported that the ionic strength 

had an effect on the measured adhesion values in a way that could not be 

explained purely by DLVO interactions.


3.5.2 Effect of Surfactant on Particle–Bubble Interactions 

During the froth flotation process, surfactant compounds are commonly 

added to the flotation chamber to modify bubble–particle 

attachment and increase mineral recovery. A number of AFM-based 

measurements have been carried out to assess the effect of surfactants in 

solution on particle–bubble interactions and hence, presumably, on flotation 

efficiency. 

Preuss and Butt [36, 48] studied the effects of adding two surfactants, 

sodium dodecyl sulphate (SDS) and dodecyltrimethylammonium bromide 

(DTAB), to solution when carrying out measurements between 

both hydrophobic and hydrophilic particles with air bubbles. When 

hydrophilic silica particles were allowed to approach the bubble in aqueous 

solution without surfactant present, repulsive forces were measured 

prior to contact, as reported previously for hydrophilic silica particles [37, 

39]. As the concentration of SDS in solution was increased, this repulsive 

force also increased and the decay length became decreased. As SDS has 

a negative charge in solution, as do the silica–water and air–water interfaces, 

the most likely explanation was that the repulsion was electrostatic 

in origin and increased with increasing quantities of SDS at the interfaces. 

When the effects of DTAB were investigated long-range forces between 

the particles and the bubbles occurred, and adhesion was observed when 

retracting the particle, most probably due to DTAB coating the silica surface 

and increasing its hydrophobicity. 

When silanized hydrophobic silica particles were used, capillary forces 

were dominant, with large adhesions on the order of 70 mN m �1 detected 

upon particle retraction [36, 48]. In the absence of SDS, small repulsive 

forces were measured on approach, probably due to electrostatic repulsion. 

When SDS was introduced, adhesion appeared to be dependent 

upon the maximum force used to press the particle into the bubble, reaching 

a threshold value of approximately 6 mN m �1 for an SDS concentration 

of 5.6 mM. Below this threshold value no adhesion was seen, with no 

hysteresis between the approach and the retract parts of the force curves, 

suggesting that the SDS was reducing the interaction between the particle 

and the bubble. As the loading force increased above the threshold, a 

jump-in event occurred and high adhesion was observed. This threshold 

force was increased, as the SDS concentration was increased as illustrated 

in Figure 3.5. When the effects of DTAB were investigated, they were 

found to follow a similar trend to that seen with SDS. At concentrations 

�6 or 12 mM, for SDS or DTAB, respectively, formation of the TPC was no 

longer observed for the load forces that were reached [36, 48]. The most 

likely explanation for this behaviour is that a surfactant film was built up 

between particle and bubble, preventing TPC formation. As the surfactant 

concentration was increased, this film would most likely be thicker and


Fthr/R/mN/m 

8 

6 

4 

2 

0 

SDS 

DTAB 

0 2 4 6 8 10 12 

Surf.conc./mM 

FIGurE 3.5 Effect of SDS and DTAB concentration on the (normalised) threshold force 

(F/R) needed to achieve a TPC with an air bubble in aqueous solution. Reprinted with permission 

from [36]. Copyright 1998 American Chemical Society. 

more stable. To make a TPC contact, the loading force would have to be 

sufficient to cause penetration of the surfactant film, characterised by the 

threshold force, which would increase with thicker surfactant films. 

Recently, force interaction measurements have been carried out 

between silica glass spheres and colloidal gas aphrons (CGAs) [49]. 

CGAs are a form of very small (�100 �m) surfactant-stabilized bubbles 

created by high shear rate flows, first described by Sebba in 1971 as 

micro-foams [50]. The use of aphrons has been proposed for a number 

of potentially useful applications. These include the flotation of fine 

mineral particles [51, 52], the treatment of particulates and contaminant 

chemicals including solvents and heavy metals from wastewater [53–56], 

treatment of soil contamination [53, 57, 58], the harvesting of microbial 

cells [59] and extraction of protein products [58, 60, 61], and the production 

of tissue engineering scaffolds [62]. Sebba proposed a multi-walled 

structure for CGAs consisting of an outer surfactant bilayer, followed by 

an internal layer of surfactant solution, in turn separated by a surfactant 

monolayer from a central gas core. Although this putative structure has 

not been confirmed conclusively, there are a number of indirect experimental 

observations which suggest that the internal structure of CGAs 

are different from those observed with conventional foams, including xray 

diffraction, and transmission electron microscopy (TEM) [58, 63].


Force, F/R (mN/m) 

A 

Force, F/R (mN/m) 

B 

1 

0.8 

0.6 

0.4 

0.2 

–150 –100 –50 

0 

0 

–0.2 

50 100 150 200 250 300 

–0.4 

–0.6 

–0.8 

–1 

1 

0.8 

0.6 

0.4 

0.2 

–0.4 

–0.6 

–0.8 

–1 

z-Displacement (nm) 

–150 –100 –50 

0 

0 

–0.2 

50 100 150 200 250 300 

z-Displacement (nm) 

FIGurE 3.6 Normalised force versus z-displacement curves obtained between aphrons 

created using SDS (A) and DTAB (B) in water. Each force curve is an average of several 

force–distance cycles (SDS � 10; DTAB � 9). In both cases a jump-in event is observed. 

However, when the glass sphere approaches the anionic SDS-stabilised aphron, a repulsive 

force is observed prior to contact, most likely due to repulsive (negative) charge interactions. 

When an identical glass probe approaches DTAB-stabilised aphrons, only attractive 

forces are seen prior to jump-in. 

Aphrons created in surfactant solutions which were either anionic 

sodium dodecyl sulfate (SDS) or cationic dodecyl trimethylammonium 

bromide (DTAB) by mixing at high sheer rates (with rotor speeds 

� 5000 rpm) were immobilised on hydrophobic HOPG and rinsed with 

an excess of high purity de-ionised water [49] to remove excess surfactant 

from solution. Aphrons were made in solutions with surfactant 

concentrations of 1 and 2 g l �1 for SDS and DTAB, respectively. Colloid 

probes consisting of glass spheres were then allowed to approach the 

surface of the aphrons (estimated bubble diameters were � 50 �m) and 

the resultant interaction forces were measured. Figure 3.6 shows example 

force measurements obtained when approaching aphrons produced

3.6 EFFECT OF LOADINg FORCE ON PARTICLE–BUBBLE INTERACTIONs 97 

using SDS and DTAB. In both cases probes became attached to the CGA 

surfaces. However, when approaching SDS CGAs, a repulsive force was 

observed prior to contact. This force was not observed with the DTAB 

aphrons. The difference is most likely due to charge repulsion effects, 

which is due to the interaction between the negatively charged glass surface 

and the negatively charged SDS. In the case of DTAB, which contains 

a positive charge in solution, only attractive forces are observed prior to 

contact. When silica was allowed to interact with CGAs in bulk flotation 

experiments, the silica was found to separate with the CGA fraction 

when using DTAB to create the CGAs, but a much smaller fraction was 

recovered when using SDS. The attachment of silica to CGAs in solution 

was modulated by the charge interactions between silica and the CGAs 

in solution, with repulsive charges preventing the attachment of the particles 

to SDS CGAs in solution. 

3.6 EFFECt oF LoADInG ForCE on 


As has been seen above in the work by Preuss and Butt, in the presence 

of surfactants [36, 39, 48], sometimes a threshold force is required to form a 

TPC contact, but there are likely to be other effects of the loading force on 

particle–bubble interactions. As the loading force is increased, deformation 

of the bubble would be expected to increase, particularly if the TPC line 

does not move over the particle surface. For other deformable surfaces, 

such as soft polymer interfaces, the maximum loading force reached has 

been observed to have a positive effect on the adhesion force [64]. This is 

not surprising, as the area of contact between the probe and the surface 

will increase as the surface becomes increasingly deformed. At small loading 

forces, where the force F


3.7 EFFECt oF HyDroDynAmICS on 


As all of the particle–bubble interaction measurements carried out 

using an AFM-based system are undertaken in a liquid environment, it 

is necessary to consider the implications of hydrodynamic forces on the 

interactions being measured. During the process of froth flotation, the 

particles and bubbles are circulated around the flotation chamber at some 

speed, and to relate what happens in this industrial process to what happens 

in AFM experiments, some measure of the effects of the speed of 

interaction between particles and bubbles necessarily has to be made. 

Nguyen and Evans [66] considered the hydrodynamic force acting on a 

sphere approaching a bubble in fluid. The hydrodynamic drag force F h 

on the particle follows the following relationship, dependent upon the 

separation distance d from the bubble surface: 

Fh RVf 

� �6π� 1 

(3.16) 

where � is the dynamic viscosity of the surrounding fluid, V the velocity 

with which the particle approaches the bubble surface (not to be confused 

with the AFM piezo-drive speed), and f 1 a correction factor which accounts 

for the deviation of the drag force from Stokes law. It is within this correction 

factor that the term for the separation distance appears and was derived by 

Nguyen and Evans to be approximated by: 

f 

1 

R 

� 1 � 

4d 

⎛ ⎡ 

⎢ ⎞ 

⎜ 

⎢ ⎝⎜ 

⎠⎟ 

⎣⎢ 

1 

0. 719⎤ 

0. 719 

⎥ 

⎦⎥ 

(3.17) 

Deformation of the bubble as the approaching particle encounters the 

thin wetting film around the bubble will lead to a reduction of V at small 

separation distances [20] relative to the driving speed. 

Nguyen et al. [12] studied the effect of the approach speed upon the 

forces obtained when a spherical glass particle approached an air bubble 

surface. In Figure 3.7 the effect on the measured force of different piezotranslation 

speeds is demonstrated. As the approach speed was increased, 

the repulsive particle–bubble forces at short separation distances were 

also increased. This was possibly due to limitations on the ability of 

the thin water film between particle and bubble to drain in the shorter 

time frames imposed by the higher approach velocities. This demonstrates 

that hydrodynamic forces were acting as an additional repulsive 

force. At low piezo-approach speeds of 0.6 �m s �1 the hydrodynamic forces 

were negligible and instead surface forces were dominant. This effect has

3.7 EFFECT OF HyDRODyNAMICs ON PARTICLE–BUBBLE INTERACTIONs 99 

AFM Measured interaction force, F (nN) 

6 

4 

2 

0 

0 

Approach speeds (µm/s) 

0.6 

3.0 

5.9 

12.2 

17.8 

27.9 

39.1 

65.4 

97.8 

100 200 300 400 500 600 

Separation distance, D (nm) 

FIGurE 3.7 Effect of the speed of approach between a particle and bubble on the measured 

forces. Reprinted from [12]. Copyright 2004, with permission from Elsevier. 

also been characterised using the colloid probe technique for a sphere 

approaching a solid confining wall in a fluid environment [67–71]. Due to 

the change in deflection of the cantilever as a result of the action of forces 

upon it, the actual velocity experienced by the particle differs from that 

applied by the piezo. A plot of the actual velocity against measured force 

and calculated hydrodynamic force as determined by Nguyen et al. [12] is 

presented in Figure 3.8. As can be seen the velocity actually decreases as 

the particle–bubble separation distance is decreased due to the increase in 

repulsive force, causing the cantilever to become deflected upwards, away 

from the bubble surface. A similar effect was observed by Aston and Berg 

[72] when approaching a droplet of n-hexadecane with a glass sphere in an 

SDS solution. It was found that the oil–water interface became dimpled on 

approach, with the distance at which this occurred increasing with increasing 

approach speed. 

Another study by Nguyen et al. [38] examined the effect of the speed 

of approach of spherical polyethylene particles on the receding contact 

angles measured, obtained from force curves as described earlier. It was 

found that at relatively high approach speeds of �10 �m s �1 , there was 

a strong influence of the approach speed on measured contact angle. 

At speeds below this there was little influence on contact angle. It was 

surmised by the authors that at the lower speeds, the measurements 

represented a ‘static’ contact angle.


Normalised force, F/R (mN/m) 

1 

0.8 

0.6 

0.4 

0.2 

Velocity 

Force 

0 

0 

0 200 400 600 800 1000 

Separation distance, D (nm) 

FIGurE 3.8 The relative velocity V and the measured (points) and hydrodynamic 

forces (line), for a piezo-movement speed of 48.8 �m s �1 . Reprinted from [12], Copyright 

2004, with permission from Elsevier. 

3.8 ConCLuSIonS 

The AFM-based colloid probe technique has been used to investigate the 

interactions between single particles and air bubbles in aqueous solution 

with the aim of increasing the basic understanding of processes dependent 

upon this type of interaction. The effect of such particle properties as the 

degree of hydrophobicity has been examined in relation to properties such 

as particle–bubble adhesion, the favourability of long-range interaction 

forces to particle–bubble attachment, as well as measured contact angles 

in a number of studies. Measurements have also begun to characterise 

the effect of force and approach speed on these interactions. As froth flotation 

is a dynamic process, an understanding of the forces and kinetics 

involved in particle–bubble attachment may be necessary to marry AFMbased 

measurements to what is happening in the flotation chamber or 

other related industrial processes. The body of literature which now exists 

is not yet complete enough to give a full insight into how particle–bubble 

interactions on the single interaction level mediate the bulk process of 

froth flotation. In addition, measurements so far utilise micro-spheres with 

an idealised geometry. Particles used in mineral separation are more likely 

to be rough and irregular and quite likely more heterogeneous, leading to 

more complexity in their attachment to bubbles. In the industrial processes, 

there are a large number of different surfactants and other chemicals used 

to modulate mineral separation, depending upon the properties of the 

minerals of interest. In the AFM-based literature, only a small number of 

commonly available surfactants have been used. On the whole, the use of 

50 

40 

30 

20 

10 

Relative velocity, U (µm/s)

LIsT OF syMBOLs 101 

AFM-based techniques to study particle–bubble interactions shows a great 

amount of promise to elucidate the properties on the level of single interactions 

which determine effects observed at the macroscopic level; however, 

there is room for a great number nevertheless of further measurements and 

experiments before a thorough understanding can be realised. However, 

the ability of the AFM and in particular the colloidal probe technique has 

a great deal of potential, due to its unique ability to measure interaction 

forces on such a small scale, to contribute greatly to the understanding of 

the underlying mechanisms in processes dependent upon the interactions 

between suspended colloids and deformable interfaces. 

LISt oF ABBrEvIAtIonS 

AFM Atomic force microscopy 

DLVO Derjaguin, Landau, Vervey and Overbeek 

DTAB Dodecyltrimethylammonium bromide 

HOPG Highly ordered pyrolytic graphite 

JKR Johnson, Kendall and Roberts theory 

PTFE Polytetrafluoroethylene 

SDS Sodium dodecyl sulphate 

TPC Three phase contact 

LISt oF SymBoLS 

c Intercept of force curve 

x Deflection m 

d Separation distance m 

D Penetration distance of particle into bubble m 

dc Particle bubble separation in contact m 

E1 Energy barrier for adhesion J 

Ek Kinetic energy of collision J 

’ Ek Kinetic energy of detachment J 

F Force N 

Fad Force of adhesion N 

FCAP Capillary force N 

Fd London dispersive van der Waals forces N


F e Electrical double layer forces N 

F h Hydrophobic force N 

k Spring constant N m �1 

k b Boltzmann’s constant (1.38 � 10 �23 ) J K �1 

k bubble Bubble spring constant N m �1 

k c Cantilever spring constant N m �1 

k m Uncorrected measured spring constant N m �1 

k ref Reference cantilever spring constant N m �1 

k tot Total spring constant of system N m �1 

P a 

P c 

P d 

Probability of adhesion 

Probability of collision 

Probability of detachment 

r Radius of TPC circle m 

R Radius of sphere m 

V Velocity of particle m s �1 

W Interaction energy J m �2 

W a Work of adhesion J 

z Distance travelled by z-piezo m 

� Immersion angle ° 

� Interfacial tension N m �1 

� c 

Slope of contact region of force curve 

� hard Slope of contact region against hard surface nA m �1 

�l Distance of probe from end of cantilever m 

� Contact angle ° 

� a Advancing contact angle ° 

� r Receding contact angle ° 

� Geodesic curvature of TPC 

� f Density of fluid Pa s 

� Line tension N m �1 

�i Imaginary component of hydrodynamic function 

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Butterworth & Co, London, 1963.

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474–480. 

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C H A P T E R 

4 

Investigating Membranes and 

Membrane Processes with 

Atomic Force Microscopy 

W. Richard Bowen and Nidal Hilal 

O U T L I N E 


4.2 The Range of Possibilities for Investigating Membranes 109 

4.3 Correspondence between Surface Pore Dimensions from 

AFM and MWCO 113 

4.4 Imaging in Liquid and the Determination of Surface Electrical Properties 116 

4.5 Effects of Surface Roughness on Interactions with Particles 120 

4.6 ‘Visualisation’ of the Rejection of a Colloid by a Membrane 

Pore and Critical Flux 123 

4.7 The Use of AFM in Membrane Development 124 

4.8 Characterisation of Metal Surfaces 126 

4.8.1 Effect of Electropolishing of Steel Surfaces 130 

4.8.2 Corrosion of Metal Surfaces 132 

4.8.3 Biofilms at Metal Surfaces 135 


Acknowledgements 136 





108 4. INvEsTIgATINg MEMbRANEs ANd MEMbRANE PROCEssEs 

4.1 InTRODUCTIOn 

Membrane processes are one of the most significant developments in 

process engineering in recent times. The worldwide annual sales of membranes 

and membrane equipment are now worth in excess of 1 billion 

Euros. Membranes find widespread application in fields as diverse as water 

treatment, pharmaceutical processing, food processing, biotechnology, 

sensors and batteries. Membranes are most usually thin polymeric sheets, 

having pores in the range from the micrometre to sub-nanometre, that act 

as advanced filtration materials. This chapter is particularly concerned 

with pressure-driven membrane processes – microfiltration, ultrafiltration, 

nanofiltration and reverse osmosis. These are usually classified according 

to the size of materials that they separate, with ranges typically given as 

10.0 � 0.1 �m for microfiltration (MF), 0.1–5 nm for ultrafiltration, �1 nm for 

nanofiltration (NF) and �1 nm for reverse osmosis (RO). 

The human imagination, including the scientific imagination, is highly 

visual. We are most easily convinced of the existence of phenomena and 

processes in the physical world if we can see them. The importance of seeing 

is deeply imbedded in language. Thus, when we finally understand 

some highly complex and abstract explanation, we may comment, ‘I see 

that now’. However, the size range of objects that the unaided human eye 

can directly observe is limited. We can use optical microscopes to extend 

the lower limit of this range down to objects of sizes comparable to the 

wavelength of light. Beyond this limit, we need to use other means to ‘see’. 

Atomic force microscopy (AFM) is one means of imaging objects of 

dimensions from about the wavelength of light to those below a nanometre. 

Thus, in the case of membranes, it is possible to visualise the membrane 

surface properties, such as pores and morphology, using AFM. 

Fortuitously, the size range of objects that may be visualised by AFM corresponds 

closely to the size range of surface features that determine the 

separation characteristics of membranes. 

However, the separation characteristics of membrane interfaces do not 

depend solely on the physical form of surface features. In liquids, surface 

electrical properties and the adhesion of solutes to membrane surfaces 

may also have profound effects on separation performance. It is thus 

exceedingly fortunate that an Atomic Force Microscope may also be used 

to determine both of these additional controlling factors. Finally, means 

may be devised to quantify all of these controlling factors in liquid environments 

that match those of process streams. 

The first intention of this chapter is to provide a concise review of the 

potential of AFM for the investigation of membranes and membrane 

processes, using examples from our own studies. The chapter will begin 

with illustrative examples that outline the range of possibilities of AFM

4.2 THE RANgE OF POssIbILITIEs FOR INvEsTIgATINg MEMbRANEs 109 

studies for membrane technology. Some more advanced topics will then 

be considered: the correspondence between surface pore dimensions 

from AFM and MWCO (molecular weight cut-off); imaging in liquid 

and the determination of surface electrical properties; effects of surface 

roughness on interactions with particles; ‘visualisation’ of the rejection 

of a colloid by a membrane pore and the use of AFM measurements in 

membrane development. The written text and technical details will be 

kept to a minimum throughout. Such details are described fully in the 

original publications. The intention is to let the images ‘speak’ for themselves! 

The second intention is to provide a short account of AFM studies 

of metal surfaces, especially stainless steel surfaces. Stainless steel is 

extensively used in the construction of membrane equipment, and the 

interaction of process streams with its surface can be a significant factor 

in the overall successful operation of the separation process. Such studies 

also have broader relevance due to the widespread use of stainless steel 

in many process industries. 

4.2 ThE RAngE OF POSSIbILITIES FOR 

InVESTIgATIng MEMbRAnES 

A membrane technologist acquiring an Atomic Force Microscope for 

the first time is best advised to begin with relatively simple measurements. 

A good starting point is to image some track-etch membranes in 

air. The pores in such membranes may also be imaged using a good optical 

microscope, which gives assurance about the images produced by 

AFM. As an example, Figure 4.1 shows an AFM image of a Cyclopore 

membrane of specified pore dimensions of 0.2 �m [1]. 

µm 

0.20 

0.10 

0.00 

3 

µm 

2 

1 

0 

0 

1 

µm 

2 

3 

% of pores 

25 

20 

15 

10 

5 

0 

0.10 0.15 0.20 0.25 0.30 0.35 

Pore size, µm 

FIgURE 4.1 AFM image and pore size distribution of Cyclopore membrane.


Shown alongside the membrane image is the derived pore size distribution. 

Such distributions may be readily obtained using commercial 

image analysis software, either automatically or manually. 

Once successful images of microfiltration membranes have been 

obtained, it is a challenge to move downwards in expected pore size or 

MWCO. Thus, Figure 4.2 shows a single pore in a PCI Membranes ES625 

ultrafiltration membrane, which has a specified MWCO of 25 000 [2]. 

The derived pore size distribution indicates a mean pore size of 5.1 nm 

with a standard deviation of 1.1 nm. This is a pore of dimensions suitable 

for separating a protein molecule. It should be noted that it is not always 

possible to image such small pores. In particular, it is necessary for the 

membrane surface roughness to have characteristic dimensions less than 

the pore dimensions for successful imaging. 

An important challenge in science is ‘to boldly go’ where no man 

(or woman) has been before. Thus, Figure 4.3 shows an image and the 

Å 

2.00 

1.00 

0.00 

120.0 

80.0 

Å 

40.0 

0 

0 

40.0 

80.0 

Å 

120.0 

% of pores 

30 

20 

10 

0 

2 3 4 5 6 7 8 9 

Pore size, nm 

FIgURE 4.2 Single pore and pore size distribution of ES625 ultrafiltration membrane. 

40 

35 

30 

Å 

2.00 

1.00 

25 

0.00 

20 

16 

15 

12 

10 

Å 8 

16 

5 

4 

0 

0 

4 

8 

12 

Å 

0 

0.0 0.5 1.0 1.5 

Pore size, nm 

2.0 

FIgURE 4.3 Single pore and pore size distribution of XP117 nanofiltration membrane. 

% of pores

4.2 THE RANgE OF POssIbILITIEs FOR INvEsTIgATINg MEMbRANEs 111 

corresponding pore size distribution of a single pore in a nanofiltration 

membrane, XP117 from PCI Membranes. 

Caution is needed here. It is only in exceptional instances that it is possible 

to obtain images of such small pores. Further, some scepticism is in 

order. The existence of pores in microfiltration membranes may be confirmed 

by optical images. It does not seem unreasonable to push the limit 

of belief in pores down to the ultrafiltration range. But in the nanofiltration 

range, we need to be especially aware of the possibility of artefacts that 

look like pores and of seeing what we wish to visualise. 

It was mentioned in Section 4.1 that an Atomic Force Microscope can 

also quantify the other key properties controlling the membrane performance. 

The crucial innovation in the determination of such properties is 

the development of colloid probes. Such probes are formed by attaching 

particles of dimensions of the order of �1 �m to the end of tipless cantilevers. 

Such attachment may be carried out using the manipulation properties 

of an Atomic Force Microscope, but greater success is achieved with 

the use of specially designed micromanipulation equipment. An example 

of a colloid probe is shown in the electron microscopy image of Figure 4.4. 

The silica colloid probe shown is at about the lower size limit for successful 

micromanipulation and subsequent measurement. 

If such probes are manipulated to approach a single point on a membrane 

surface in a controlled manner in an electrolyte solution, it is possible 

to directly quantify the electrical double layer interactions between probe 

and membrane, also shown in Figure 4.4, for two solutions of differing ionic 

strengths. Such electrical interactions are very important in determining the 

rejection of colloids and biological macromolecules during ultrafiltration. 

The adhesion of process stream components to membranes also has an 

important influence on membrane performance. Ideally, such adhesion 

(F/R) / (mN/m) 

20 

15 

10 

5 

10-4 10 

M NaCl, pH8 

-1 M NaCl, pH8 

0 

0 5 10 15 20 25 30 35 40 

Distance / nm 

FIgURE 4.4 SEM image of a 0.75 �m silica sphere attached to a tipless AFM cantilever 

and force distance curves for the approach of the probe to a Cyclopore microfiltration membrane 

in NaCl solutions at pH 8. (F is force and R is sphere radius.)


–3 

1000 1200 1400 1600 1800 2000 

Piezo displacement [nm] 

should be avoided. As an example, Figure 4.5 shows a polystyrene colloid 

probe and data for the retraction of such a probe after it has been 

pushed into contact with membrane surfaces [3]. 

The depths of the depressions of the curves in Figure 4.5 give direct 

quantification of the adhesion of the probes to the surfaces. The ES404 

membrane was an existing commercial membrane and the XP117 membrane 

is a development membrane designed to have lower fouling properties 

(both membranes are PCI Membranes). The development membrane 

had significantly lower adhesion and hence significantly lower fouling 

potential than the existing membrane. 

Ultrafiltration membranes are used particularly for the processing of 

solutions of biological macromolecules. Such molecules are too small to 

immobilise singly on a cantilever. However, by adsorbing such molecules 

onto colloid probes, it is possible to measure their adhesion to membrane 

surfaces. Such a protein (BSA – bovine serum albumin)-modified probe 

and the corresponding adhesion data for two membranes is shown in 

Figure 4.6 [4]. 

The data shows that the protein-modified probe has significantly 

lower adhesion to the development membrane, XP117, than to the existing 

commercial membrane, ES404, and hence the modified membrane 

has significantly lower fouling potential in the processing of such protein 

solutions. 

Membranes are frequently used to process biological cell dispersions. 

In order to elucidate such processes, it has been proved possible 

to immobilise single cells at tipless AFM cantilevers, creating cell probes, 

whilst maintaining the viability of such a cell, Figure 4.7 [5]. 

Such cell probes allow the direct measurement of the adhesion of biological 

cells to membranes. Interpretation of the data for such cell probes 

F/R [mN/m] 

5 

4 

3 

2 

1 

0 

–1 

–2 

ES 404 

XP 117 

FIgURE 4.5 SEM image of a 11 �m polystyrene sphere attached to a tipless AFM cantilever 

and force versus piezo displacement plot (retraction) for two membranes in 10 �2 M 

NaCl solution at pH 8.0 (ES404, conventional; XP117, modified). 

D 

C 

B 

A' 

A

4.3 CORREsPONdENCE bETwEEN sURFACE PORE dIMENsIONs FROM AFM ANd MwCO 113 

F/R [mN/m] 

–30 

0 200 400 600 800 


is more difficult than for colloid or modified colloid probes as the cell can 

distort during the measurements. However, the data show that the XP117 

development membrane has lower adhesion, and hence lower fouling 

propensity, also for yeast cells. 

4.3 CORRESPOnDEnCE bETWEEn SURFACE PORE 

DIMEnSIOnS FROM AFM AnD MWCO 

From a practical point of view, the choice of ultrafiltration membranes 

for a particular process is usually defined in terms of MWCO, defined 

such that solutes of such molecular weight would be 90% rejected by the 

30 

20 

10 

0 

–10 

–20 

Modified membrane (2) 

Conventional membrane (1) 

FIgURE 4.6 SEM image of a BSA-coated silica sphere attached to a tipless AFM cantilever 

and force versus piezo displacement plot (retraction) for two membranes in 10 �2 M 

NaCl solution at pH 5.0 (conventional, ES404; modified, XP117). 

Force [nN] 

20 

15 

10 

5 

0 

–5 

C 

B 

Conventional membrane (1) 

Modified membrane (2) 

–10 

0 100 200 300 400 500 


FIgURE 4.7 SEM image of a yeast cell (Saccharomyces cerevisiae) attached to a tipless 

AFM cantilever – a cell probe – and force versus piezo displacement plot (retraction) for 

two membranes in 10 �2 M NaCl solution at pH 5.0 (conventional, ES404; modified, XP117).


membrane. Care is required in the use of MWCO as rejection can depend 

on other factors such as charge and molecular shape, but it remains an 

extensively used parameter. It is possible to estimate the mean pore diameter 

of membranes from rejection data such as MWCO through the use 

of an appropriate mathematical expression. As MWCO is a historically 

important measure and AFM a relatively new technique, it is pertinent to 

investigate the correspondence between the data respectively obtained. 

Such an investigation has been carried out for a series of membranes 

with MWCO in the range 1000–10 000 (Desal-G, Osmonics) [5]. Images 

of membranes obtained in air at the extremes of this range, GE (1000) 

and GN (10 000), are shown in Figure 4.8. The higher MWCO membrane 

is noticeably rougher. Indeed, there is a significant increase in surface 

roughness throughout the range, as shown by the data in Table 4.1. 

From such images, it is possible to determine the surface pore diameter 

distributions of the membranes. Data is given in Table 4.2, together with 

the mean pore diameters from MWCO, using three differing mathematical 

Å 

268 

134 

0 

3 

2 

300 

µm 

Å 

3.00 

2.00 

1.00 

0.00 

1 

200 

Å 

GE membrane 

100 

0 0 

1 

µm 

2 

3 

3 

2 

µm 

1 

GN membrane 

0 0 

GE membrane GN membrane 

Å 

2.00 

0 0 

100 

Å 

200 

300 

300 

200 

100 

0 0 

FIgURE 4.8 AFM images of two Desal G membranes, GE (MWCO 1000) and GN 

(MWCO 10 000), at low resolution (above) and high resolution (below). 

1.00 

0.00 

Å 

1 

100 

µm 

2 

Å 

200 

3 

300

4.3 CORREsPONdENCE bETwEEN sURFACE PORE dIMENsIONs FROM AFM ANd MwCO 115 

expressions. Depending on the expression used, the ratio of the mean pore 

diameters obtained from MWCO data and AFM measurements was in the 

range 1.04–2.42. Agreement between the diameters obtained in the two ways 

was best for the membranes with the lowest MWCO values. The two measurements 

are probing the membrane properties in different ways, but the 

overall correlation is encouraging. 

However, AFM has the important advantage of providing a measure 

of pore size distribution. This is indicated in Table 4.2 by the 

standard deviations. A full distribution for one of the membranes is given 

in Figure 4.9. 

Knowledge of such distributions is very important if the membrane is 

to be selected for a fractionation process, where a narrow distribution is 

highly desirable. Further, theoretical modelling to predict membrane process 

performance often assumes a log-normal distribution of pore sizes. 

Figure 4.9 shows that this is a reasonable assumption in this case. 

TAbLE 4.1 surface Characteristics of desal g Membranes Over Areas of 

3 �m � 3 �m (R p−v, Peak to valley distance; Rms, Root-Mean-square). 

Membrane MWCO R p–v (nm) Rms roughness (nm) 

GE 1000 26.6 3.6 

GH 2500 58.7 8.4 

GK 3500 53.9 8.4 

GM 8000 63.7 9.2 

GN 10 000 88.1 11.7 

TAbLE 4.2 Pore diameters for desal g-series Membranes Obtained from AFM 

Measurements and MwCO. 

AFM mean pore 

diameter Mean pore diameters from MWCO (nm) 

Membrane (nm) * Ex. 1 Ex. 2 Ex. 3 

GE 1.8 (�0.3) 1.9 2.4 2.0 

GH 2.2 (�0.5) 2.6 3.8 3.2 

GK 2.5 (�0.5) 3.0 4.4 4.2 

GM 2.8 (�0.7) 4.4 6.4 6.8 

GN 3.1 (�0.9) 4.8 7.2 7.6 

* Numbers in brackets are standard deviations.


Fraction of pores counted 

0.16 

0.14 

0.12 

0.10 

0.08 

0.06 

0.04 

0.02 

AFM distribution 

Theoretical distribution 

0.00 

0.00 

2.0 2.5 3.0 3.5 4.0 4.5 5.0 

Pore diameter/nm 

FIgURE 4.9 AFM pore size distribution for Desal GM membrane and theoretical lognormal 

distribution. 

4.4 IMAgIng In LIqUID AnD ThE DETERMInATIOn OF 

SURFACE ELECTRICAL PROPERTIES 

For membranes that are used in liquid systems, it is very useful to 

have the possibility of imaging in a solution corresponding to the processing 

conditions of pH and ionic content. An Atomic Force Microscope 

gives great control of imaging protocols, allowing investigation of the 

procedures that give the best membrane images, in particular the imaging 

force. Figure 4.10 shows the force of interaction between an AFM tip 

and a Cyclopore membrane of specified pore diameter 0.1 �m in solutions 

at constant pH but varying ionic strength [6]. 

It may be seen that the range of the interaction increases greatly as the 

ionic strength decreases in accordance with electrical double layer theory. It 

is then possible to image the membrane using a force at any point on the 

curves in Figure 4.10. Two series of such images, one at various forces at 

constant ionic strength and the other at approximately constant force at various 

ionic strengths, are shown in Figure 4.11. It may be seen that the quality 

of the images improves with increasing imaging force and with increasing 

ionic strength. The derived pore diameter distributions also vary with the 

imaging conditions, as shown in the corresponding graphs in Figure 4.11 [7]. 

The reason for this variation may be understood from Figure 4.12, 

which shows calculated isopotential lines for a 10 �1 M solution and a 

10 �4 M solution, respectively. 

0.16 

0.14 

0.12 

0.10 

0.08 

0.06 

0.04 

0.02 

Probability density function fR(r)

4.4 IMAgINg IN LIqUId ANd THE dETERMINATION OF sURFACE ELECTRICAL 117 

Force (nN) 

50 

40 

30 

20 

10 

NaCl 10 –1 M 

NaCl 10 –2 M 

NaCl 10 –3 M 

NaCl 10 –4 M 

0 

0 5 10 15 20 25 30 35 

Distance (nm) 

FIgURE 4.10 Force versus distance curves for the approach of an AFM tip to a 

Cyclopore microfiltration membrane in NaCl solutions of various ionic strengths at pH 6.5. 

Roughly understood, the imaging tip will follow an isopotential line 

during the imaging process. At the high ionic strength, all of the calculated 

lines lie close to the membrane surface (shaded, spinning the image 

360° out of the plane of the paper would generate a pore). At the lower 

ionic strength, some of the isopotential lines lie far from the surface, so 

a clear, veracious pore image would not be obtained when such a line is 

followed, as would be the case at low imaging forces. In conclusion, the 

best imaging conditions in ionic solutions are at high imaging force and, 

if possible and appropriate, at high ionic strength. 

Though most membrane technologists now recognise the important 

contribution of membrane surface electrical properties in defining the 

separation characteristics, there remains confusion as to how best to 

describe and quantify such interactions. There is an unfortunate tendency 

in the applied membrane literature to use the terms ‘charge’ and ‘potential’ 

loosely, almost interchangeably. There is also a regrettable lack of 

precision in the interpretation of membrane streaming potentials, which 

are the basic data most commonly used to quantify membrane surface 

electrical properties. The interpretation of streaming potential data can 

be complex even for perfectly smooth and chemically uniform planar 

surfaces. Most membrane surfaces have roughness comparable to electrical 

double layer dimensions, so along-the-surface-membrane streaming 

potential data give only some average property. Through-the-membrane 

streaming potential data may only be usefully interpreted in comparison


Imaging force = 4.35 nN 

NaCl 10 -1 

2 

µm 

1 

% 

A 

0 

2 

1.5 

µm 1 

0.5 

0 

50 

40 

30 

20 

10 

0 

Imaging force = 33 nN 

NaCl 10 -4 

0 

0.5 

1 

µm 

IF = 4.4 nN 

10 -1 M 

0 

0.05 0.10 


0.15 

2 

1.5 

1 µm 

2 


NaCl 10 -1 

2 

µm 

A B C 


NaCl 10 -3 

2 

1.5 

µm 1 

0.5 

0 

0 

0.5 

1.5 

1 

µm 

D E F 

% 

50 

40 

30 

20 

10 

IF = 33.0 nN 

10 -4 M 

0 

0.05 0.10 0.15 0.20 


% 

% 

50 

40 

30 

20 

10 

1 

0 

0 

with numerical double layer calculations, as pore diameters are often less 

than the characteristic electrical double layer dimensions. 

Fortunately, AFM, in conjunction with the colloid probe technique, 

offers an alternative means of membrane surface electrical properties 

characterisation. If a colloid probe is approached towards a surface, it 

is possible to quantify the force of interaction. Typical data is shown in 

Figure 4.13 for a Desal DK membrane, which is one of the least rough 

membranes [7]. 

1 

µm 

IF = 12.9 nN 

10 -1 M 


B C 

IF = 33.1 nN 

10 -3 M 

0 

0.05 0.10 0.15 


D E F 

50 

40 

30 

20 

10 

0 

0.05 0.10 0.15 

2 

2 

% 

50 

40 

30 

20 

10 


NaCl 10 -1 

2 

µm 

1 

0 


NaCl 10 -2 

2 

1.5 

µm 1 

0.5 

0 

0 

0 

IF = 33.8 nN 

10 -1 M 

0.5 

0 

0.05 0.10 0.15 


IF = 33.2 nN 

10 -2 M 

0 

0.05 0.10 0.15 


1 

µm 

1 

1.5 

µm 

FIgURE 4.11 AFM images of a Cyclopore membrane in electrolyte solutions. (a)–(c) at 

various forces in 10 �1 M NaCl solution; (c), (d)–(f) at approximately constant force at various 

ionic strengths. All data at pH 6.5 (IF-imaging force). 

% 

50 

40 

30 

20 

10 

2 

2

4.4 IMAgINg IN LIqUId ANd THE dETERMINATION OF sURFACE ELECTRICAL 119 

F 

A 

A B 

0.3 

0.4 

C D 0.7 

0.4 

0.1 

0.5 

(a) 

C D 

F E 

FIgURE 4.12 Calculated isopotential lines at the entrance to a membrane pore of diameter 

0.1 �m. (a) 10 �1 M solution, (b) 10 �2 M solution. 

F/R/mN/m 

4 

2 

0 

0 20 40 

B 

Distance/nm 

(b) 

0.6 

0.7 

0.9 

0.8 

AFM data 

Best fit constant potential 

Best fit constant charge 

FIgURE 4.13 Best-fit solutions of theoretical force distance curves to AFM experimental 

force distance data for a Desal membrane in 10 �3 M NaCl. 

E


Moreover, if the surface potential or surface charge of the colloid has 

been determined and the solution is of defined ionic content, it is possible 

to calculate the potential or charge of the surface under investigation 

by matching the experimentally obtained curves to theoretical calculations 

on the basis of electrical double layer theory. In the example shown, 

the best-fit membrane surface charge was �0.00114 C m �2 and the bestfit 

membrane surface potential was �64 mV. Furthermore, an important 

advantage of the colloid probe technique is that it allows exploration 

of variations in surface electrical interactions at different points on the 

membrane surface, as the following section shows. 

4.5 EFFECTS OF SURFACE ROUghnESS On 

InTERACTIOnS WITh PARTICLES 

Surfaces are usually imaged using sharp tips in order to produce 

images with the highest possible definition. However, from a processing 

viewpoint, an important factor is how process stream components such as 

solutes and colloidal particles interact with the surface. If a surface has feature 

variations that have dimensions comparable with those of the process 

stream components, then such interactions may show variations at different 

locations on the surface. An effective way of gauging such effects is to 

image the surface with an appropriate stream component, e.g. a particle 

that is immobilised to form a colloid probe. Figure 4.14 shows results for 

a reverse osmosis membrane (AFC99, PCI Membranes) imaged in saline 

solution with first a sharp tip and then a 4.2 �m silica sphere [8]. 

µm 

0.4 

0.2 

4 

0 

3 

P–v = 560 nm 

Rms = 66nm 

2 

µm 

1 1 

0 0 

2 

µm 

A B 

3 

4 

µm 

0.16 

0.12 

0.2 

0.04 

4 

0 

3 

2 

µm 

P–v = 186 nm 

Rms = 21nm 

1 1 

0 0 

FIgURE 4.14 AFC99 membrane imaged with a tip (A) and with a 4.2 �m colloid probe 

(B) (P–v, peak to valley; Rms, root mean square). 

2 

µm 

3 

4

4.5 EFFECTs OF sURFACE ROUgHNEss ON INTERACTIONs wITH PARTICLEs 121 

The membrane surface features are still apparent but less well defined 

in the colloid probe image. This is a rather rough membrane showing 

clear peaks and valleys. Following imaging, it is possible to position 

the colloid probe at any point on the surface to quantify colloid–surface 

interactions. Figure 4.15 shows long-range electrostatic interactions quantified 

at peaks and valleys respectively, and some analysis of the data is 

presented in Table 4.3. 

Both the magnitude and range of the electrical double layer interactions 

on the peaks are greatly reduced compared to that in the valleys. In 

both cases, the range is very different from that at a planar surface, both 

experimental – data for mica is shown for comparison – or theoretical, 

the Debye length. It is also possible to quantify the adhesive interaction 

between colloid probe and membrane surface at different locations, as 

shown in Figure 4.16 and Table 4.4. 

F/R/mN/m 

10 

1 

AFC99, peaks 

10 –1 M 

10 –2 M 

10 –3 M 

0.1 

0 10 20 

Distance/nm 

30 40 

F/R/mN/m 

10 

1 

AFC99, valleys 

10 –1 M 

10 –2 M 

10 –3 M 

0.1 

0 10 20 

Distance/nm 

30 40 

FIgURE 4.15 Long-range electrostatic interactions at peaks and valleys for an AFC99 

membrane at various ionic strengths in NaCl solutions (F, force; R, sphere radius). 

TAbLE 4.3 Effective Experimental decay Lengths for Approach Curves between 

silica Colloid Probe and AFC99 Membrane and Mica, and debye Length. 

Effective decay lengths (nm) 

[NaCl] (M) Membrane peak Membrane valley Mica Debye length (nm) 

10 �3 7.7�1.4 12.1�1.5 9.2�0.5 9.6 

10 �2 3.2�0.6 6.8�1.2 3.5�0.3 3.1


The adhesion of the colloid probe is markedly lower at the peaks on 

the membrane surface than in the valleys, with the difference increasing 

with decreasing salt concentration, and reaching a factor of more than 20 

in 10 �3 M solution. The wide variation in interactions shows that theoretical 

descriptions of membrane fouling need to take surface morphology 

into explicit account. Further, the results show that the selection of membranes 

for the filtration of specific process streams would benefit from an 

assessment of the size of likely foulants and the membrane roughness, 

especially the periodicity of the roughness. Fouling could be minimised 

F/R / mN/m 

6 

4 

2 

0 

–2 

–4 

–6 

Peak 

Valley 

–8 

0 50 100 150 

Separation distance / nm 

FIgURE 4.16 Adhesion of a silica colloid probe at a peak and a valley on an AFC99 

membrane in 10 �3 M NaCl solution (pull-off force). 

TAbLE 4.4 Normalised Adhesion Forces for silica Colloid Probes and AFC99 

Membrane. 

Surface type [NaCl] (M) F/R (mN/m) 

Membrane peak 10 �3 �0.3 (�0.17) 

10 �2 �1.4 (�0.43) 

10 �1 �2.3 (�0.48) 

Membrane valley 10 �3 �6.5 (�2.2) 

10 �2 �8.1 (�3.5)

4.6 ‘vIsUALIsATION’ OF THE REjECTION OF A COLLOId by A MEMbRANE PORE 123 

by using membranes with roughness such that only adhesion at peaks is 

possible – where the effects of cross-flow are also maximum. 

4.6 ‘VISUALISATIOn’ OF ThE REjECTIOn OF A COLLOID 

by A MEMbRAnE PORE AnD CRITICAL FLUx 

One of the most useful practical operating concepts for membrane processes 

is that of a critical filtration flux or critical operating pressure. These 

critical parameters are such that below such critical values, rejection will 

occur and fouling will be minimum and above these critical values, transmission 

and fouling may take place. For colloidal particles, the critical 

values may arise as a balance between the hydrodynamic force driving 

the solutes towards a membrane pore and an electrostatic (electrical 

double layer) force opposing this motion. 

Science fiction writers have imagined tiny probes travelling, for example, 

through the human body, which would allow us to visualise hidden microscopic 

phenomena. Such probes remain figments of the imagination. 

However, a colloid probe moving along a membrane surface can allow us to 

visualise how a colloidal particle would ‘see’ such a surface, Figure 4.17 [9]. 

Figure 4.17 shows how a 0.75 �m silica colloid probe ‘sees’ the pores in 

a 1.0 �m Cyclopore membrane in solutions of two ionic strengths when 

imaged in each case with an applied force of 4.6 mN m –1 . It is only at the 

highest ionic strength that the pores are clearly apparent, for at the lowest 

ionic strength, such a force is experienced too far from the membrane surface 

for the electric field to still show sufficient evidence of membrane 

porosity. Cases where the process stream component dimensions are close 

to those of the membrane pores should preferably be avoided as rapid 

pore blocking may occur if the critical flux or pressure is exceeded. Such 

6 

4 

µm 

6 

4 

µm 

2 

6 

2 

0 

2 

4 

µm 

0 

0 

FIgURE 4.17 Imaging a 1.0 �m Cyclopore membrane with a 0.75 �m colloid probe, in 

0.1 M NaCl, pH 8 (left); in 0.0001 M NaCl, pH 8 (right). Normalised imaging force 4.6mN m –1 . 

0 

2 

4 

µm 

6


Flux / ms –1 

0.0006 

0.0005 

0.0004 

0.0003 

0.0002 

0.0001 

0.0000 

0 5 10 15 20 25 

Time / min 

250 kPa 

50 kPa 

FIgURE 4.18 Filtration fluxes as a function of time for filtration of particles very close 

in dimensions to the pore dimensions. Silica particles, 0.001 M NaCl, pH 6.0, mean particle 

diameter 86 nm, mean pore diameter 85 nm, calculated critical pressure � 130 kPa. 

conditions may, however, be theoretically predicted. Thus, Figure 4.18 shows 

the time dependence of flux for such a case where the critical pressure is calculated 

to be 130 kPa. Above this pressure, there is a rapid decrease in flux 

with time, but below this pressure, only a very gradual flux decrease occurs. 

4.7 ThE USE OF AFM In MEMbRAnE DEVELOPMEnT 

The ability of AFM to guide the development of improved membranes 

has been shown in the development of polysulphone-sulphonated 

poly(ether ether) ketone (PSU/SPEEK) blend membranes. The aim of the 

work was to develop highly charged membranes with correspondingly 

low adhesion characteristics and high critical fluxes [10]. The SPEEK provides 

negative charges, as shown by the structure in Figure 4.19. 

One great benefit of SPEEK is that it acts as a pore formation–promoting 

agent. This gives membranes high porosity and high fluxes, as shown by the 

increase in water flux, with increasing SPEEK content shown in Figure 4.20. 

The increase in porosity may be directly confirmed by high-resolution 

images of an unmodified PSU membrane and a PSU/SPEEK membrane 

with 5% of the charged polymer, Figure 4.21.

4.7 THE UsE OF AFM IN MEMbRANE dEvELOPMENT 125 

CH 3 

O C O S 

CH3 

PSU 

O O C 

SO 3H 

SPEEK 

FIgURE 4.19 Structures of polysulphone and sulphonated poly (ether ether) ketone. 

Jw / ms –1 

1.2e−4 

1.0e−4 

8.0e−5 

6.0e−5 

4.0e−5 

2.0e−5 

P-O 

P-P 

S0.5-20 

S2-20 

S5-20 

ΔP / kN m –2 

0.0e+0 

0 100 200 300 400 500 600 

FIgURE 4.20 Water flux as a function of applied pressure for five membranes of various 

percentages of SPEEK. P-O and P-P: 0%; S0.5-20: 0.5%; S2-20: 2.0%; S5-20: 5%. 

The adhesion of a range of colloid probes, both inorganic and biological, 

is greatly reduced at the PSU/SPEEK membranes, as shown by the 

data in Table 4.5. 

Such low adhesion forces show that the membranes are well suited to 

many types of separation. The removal of humic acid has been investigated 

as an example of a challenging separation. The blend membranes 

O 

O 

O 

n 

n


300 

200 

Å 

100 

0 0 

100 

Å 

200 

300 

gave very good separation with little fouling. By quantification of the 

fraction of humic acids deposited during filtration, it was possible to 

show that both planar (S5-20) and tubular (T5-20) versions of the membranes 

showed high critical flux values, whereas membranes already in 

commercial use for such separations (CA202 and ES404, PCI Membranes) 

did not show such a favourable property, Figure 4.22 [11]. 

To allow for the different membrane geometries, the data in Figure 4.22 

is expressed as critical Peclet numbers (J/k, where J is the flux and k is 

the mass transfer coefficient). The critical Peclet numbers were 4.6 and 

6.4 for the planar and tubular membranes respectively. Further details of 

the development of PSU/SPEEK membranes are given in Chapter 5. 

4.8 ChARACTERISATIOn OF METAL SURFACES 

The surface properties and morphology of process equipment surfaces 

are of fundamental importance in the fulfilment of their purpose and 

300 

200 

Å 

100 

0 

100 

200 

Å 

FIgURE 4.21 High-resolution images of unmodified membrane (left) and membrane 

modified with 5% SPEEK (right, S5-20). 

TAbLE 4.5 Normalised Adhesion Forces for a Range of Colloid Probes at a PsU/ 

sPEEK Membrane (s5-20). 

Materials Mean F/R (mN m �1 ) 

SPEEK/PSU PSU 

Silica 0.84�0.35 6.5�0.8 

Cellulose 0.51�0.23 2.2�0.32 

Latex 2.1�0.52 14.3�0.8 

BSA 1.4�0.64 12.3�1.4 

Yeast 3.2�0.85 9.5�1.5 

300

Dfractional 

0.18 

0.16 

0.14 

0.12 

0.10 

0.08 

0.06 

0.04 

0.02 

4.8 CHARACTERIsATION OF METAL sURFACEs 127 

CA202, ES404 

S5-20 

T5-20 

0.00 

0 5 10 15 

JHA / k 

20 25 30 

FIgURE 4.22 Fractional deposition of humic acids at different operating fluxes. The 

intercepts on the x-axis indicate the critical fluxes. 

applications in (bio) process industries. Many environments to which 

they may become exposed are potentially corrosive, and thus more 

corrosion-resistant surfaces may have greater operational lifetimes. In 

addition, surfaces may become fouled, leading to a reduction in operating 

efficiency, especially for surfaces involved in the desalination and 

water treatment industries. This section will concentrate on the use of 

AFM to characterise the surface features and morphology of metal surfaces 

of interest in process engineering applications. 

One of the most commonly used materials in process equipment is 

stainless steel in various forms. In Figure 4.23, by way of example, are 

shown three 3-dimensional 50 � 50 �m scans of different steel surfaces of 

difference roughness characteristics, imaged in air [12]. 

These are: (a) a ‘highly polished’ stainless steel surface with an optically 

fine finish, (b) the surface of a stainless steel sample disk, such as 

that commonly used for affixing AFM samples and (c) a sample stub 

similar to that in (b), which has undergone significant pitting owing to 

corrosion. Surface (b) contains ridges caused by the mechanical polishing 

of the surface, which are not visible in (a). For the corroded sample, 

there is clearly a much greater variation in the height of surface 

features and a greater number of asperities. This can be seen from the 

roughness parameters obtained from the height data contained in these


50 µm 

A 

50 µm 

B 

50 µm 

C 

25 µm 

25 µm 

25 µm 

0 µm 

0 µm 

0 µm 

0 µm 

0 µm 

0 µm 

25 µm 

25 µm 

25 µm 

726.59 nm 

0 nm 

50 µm 

1.47 µm 

0.73 µm 

0 µm 

50 µm 

3.56 µm 

1.78 µm 

0 µm 

50 µm 

FIgURE 4.23 3D topographic images of surfaces with three different grades of roughness.


TAbLE 4.6 surface Characteristics Obtained from AFM Images. 

Surface Area Ra (nm) RMS (nm) Average height (nm) Maximum range (nm) 

(a) 38.3 49.5 361.1 726.6 

(b) 124.3 170.1 785.4 1407.5 

FIgURE 4.24 SEM image of a CaCO 3 crystal mounted as a probe on the apex of an 

AFM cantilever. 

images. Table 4.6 shows surface characteristics obtained from such 

AFM images. 

The differences in the roughness average (Ra) and root mean square 

roughness (RMS) show that the statistical variation in height of the 

individual points in each image becomes greater from sample (a) to (c), 

whilst the average height and maximum range show that the magnitude 

of the variations in height, and hence size, of the surface features is much 

greater from sample (a) to (c). 

Adhesion measurements were taken with a CaCO 3 crystal, Figure 4.24, 

at five different points on the sample surface, with a total of approximately 

100 measurements per sample, and mean adhesion values were calculated.


Figure 4.25 shows a summary of the adhesion data measured between 

the probe and each of the stainless steel surfaces of interest. 

As can be seen, sample (c) has the lowest adhesion value measured, 

with the probe detaching at a mean force of 65.5 nN. Samples (b) and (a) 

showed higher adhesion, with values of 99.3 and 83.2 nN, respectively. 

As a general rule, roughness on two interacting surfaces reduces the area 

of contact between these surfaces, which would be expected to lead to 

a decrease in the measured adhesion. This could explain the increase 

in adhesion seen with surfaces (b) and (a) compared with the relatively 

rough surface (c). However, the least rough sample (a) has a lower adhesion 

than that of sample (b). If there were a simple relationship between 

the roughness of the surfaces and adhesion, this would not be expected 

to be the case. However, the relationship between roughness and adhesion 

is not easily defined and can be dependent upon the length scales 

of the roughness on the individual surfaces as well as the geometry of 

interaction of the surfaces. In some cases, if the length scales of the probe 

or asperities on the probe are similar to the roughness of the surface, it 

could be possible for an increased contact area to be achieved [13–16]. 

4.8.1 Effect of Electropolishing of Steel Surfaces 

Electropolishing is a process of dissolving the very top layer of a metal 

surface to bring about an increase in the optical brightness or reflectivity 

of a surface by the reduction of surface roughness. One advantage of this 

over polishing of surfaces by mechanical means is the absence of defects 

in the surfaces due to scratches. As the characterisation of the roughness 

Mean adhesion (nN) 

120 

100 

80 

60 

40 

20 

0 

Polished steel Unpolished steel 

sample surface 

Corroded steel 

FIgURE 4.25 Summary of measured adhesion values between a calcium carbonate colloid 

probe and three steel sample surfaces.


of surfaces at fine levels of detail is easily accomplished by AFM imaging, 

the monitoring of the polishing of surfaces is an obvious application. 

Abbot and co-workers used AFM both in air and in situ in liquid to 

monitor the changes in morphology over time of a stainless steel surface 

during electropolishing with an ionic liquid [17]. Roughness values, 

described by maximum z-height, were 597 and 88 nm for the unpolished 

and polished surfaces respectively. As the z-max figures for the unpolished 

surface were likely to be greater than would be expected owing to the surface 

not being flat, the authors also calculated roughness as a percentage 

difference in the flat scanning area versus the actual surface area of the 

sample. This yielded roughness values of 7.9% for the unpolished surface 

and 0.2% for the polished surface. It was also noted that a trough was seen 

to have been etched out at the boundary between the polished and unpolished 

areas, varying in depth from 1–2 �m, Figure 4.26. 

y / µm 

A 

70.0 

60.0 

50.0 

40.0 

30.0 

20.0 

10.0 

10.0 20.0 30.0 40.0 50.0 60.0 

x / µm 

Height/nm 

C 

500 

0 

–500 

–1000 

–1500 

–2000 

–2500 

Height/nm 

B 

500 

0 

–500 

–1000 

–1500 

–2000 

–2500 

10.0 20.0 

30.0 

40.0 

50.0 60.0 

70.0 

y / µm 

(x = 35.6µm) 

y / µm 

0.0 

10.0 

20.0 

30.0 

40.0 

50.0 

60.0 

70.0 

10.0 

20.0 

30.0 

40.0 

50.0 

60.0 

FIgURE 4.26 AFM images obtained at the transition between polished and non- 

polished areas of a stainless steel surface. (a) and (b) show the same areas in 2D and 3D 

modes. Unpolished surface is flat but has high roughness, whereas the polished surface 

is relatively smooth, but still shows large height variations. At the interface is an etched 

trench. (c) shows a line profile from the image, with the unpolished section on the left and 

polished on the right. Reproduced from [17]. 

x / µm


Vignal et al. [18] also studied the electropolishing of steel surfaces 

using the AFM. They observed that under a specific set of conditions 

(in perchloric acid and monobutyl ether), a very regular network of hexagonal 

cells of approximately 100 nm periodicity and 10 nm depth was 

observed, Figure 4.27. 

This hexagonal pattern was described as being extremely sensitive 

to the applied voltage and was explained as being ‘prints of convective 

cells…localised in a resistive sub-layer of 100 nm thickness in the viscous 

shell’ [18]. 

4.8.2 Corrosion of Metal Surfaces 

Almost all metal surfaces at some point in their lifetime either routinely 

or sporadically come into contact with corrosive media, whether 

it be aqueous solutions of high ionic strength or solutions of low pH. As 

a result, their behaviour when coming into contact with such chemicals 

and their ability to withstand corrosion play a significant part in their 

lifetime, durability, efficiency and appearance. 

One of the most common corrosive liquids present in the environment 

are aqueous NaCl solutions. Equipment used in the desalination industry, 

food processing and any equipment or structures in the maritime or nearmaritime 

environment will routinely come into contact with salt water, 

not to mention the corrosive effect on cars and roadside installations due 

500 nm 

FIgURE 4.27 Image obtained by AFM of regular hexagonal cells on steel surface 

formed after electropolishing, observed by Vignal et al. [18].


to salt spray from roads during winter. Sanchez and colleagues [19] examined 

the early stages of corrosion of high-strength steel in dilute (50 mM) 

solutions of NaCl. The steels examined were of the type used for the reinforcing 

of concrete structures, which are prone to corrosion when exposed 

to salt water due to the porous nature of the concrete and consisting of 

ferrite and cementite. The authors scanned the same area of the steel surface 

for over 2 h and observed changes in the surface morphology due to 

interaction with the corrosive media. Snapshots of the sample at different 

times are shown in Figure 4.28. 

Initially (t � 0) the polishing marks and scratches are still visible, but 

disappear after 50 minutes, when the surface was observed to be increasingly 

rough as the growth of oxides on the surface occurred. After approximately 

50 min, and later, a series of ridges were observed to appear. The 

authors concluded that this was the lamellar structure of pearlite (the 

mixture of ferrite and cementite phases) appearing as the ferrite matrix 

was selectively attacked by the salt solution. The change in the surface 

roughness was monitored as a function of time, allowing the quantitative 

assessment of corrosion of the surface, Figure 4.29. 

Z: 24.1nm 

X: 5.0µm 

A B 

Z: 40.1nm 

X: 5.0µm 

C D 

Z: 21.6nm 

Z: 151.8nm 

X: 5.0µm 

X: 5.0µm 

FIgURE 4.28 Steel surface after varying lengths of exposure to 50 mM NaCl solution. 

(a) 0 min; (b) 30 min; (c) 50 min; (d) 2 h 15 min. Reproduced from [19].


Surface roughnes (nm) 

1.6 

1.4 

1.2 

1 

0.8 

0.6 

0.4 

0.2 

0 

First 

stage 

Second 

stage 

y = –0.4907x 2 + 2.2621x–1.1032 

R 2 = 0.9906 

0 0.5 1 1.5 2 

Time (h) 

FIgURE 4.29 Change in roughness of steel surface over time during exposure to NaCl 

solution. Reproduced from [19]. 

It is apparent that the roughness of the surface increased in two stages. 

In the first stage, no significant roughness increase was observed. After 

about 35 min, the roughness increased at a rapid rate, which could be fitted 

by a simple polynomial expression. The authors attributed the first stage to 

the formation of a thin layer of corrosion products, whilst the second stage 

was due to a selective attack of the ferrite phase of the steel. 

Other studies have concentrated on the corrosion of surfaces due to 

more aggressive corrosive agents. Wang et al. [20] studied the corrosion 

of stainless steel over a number of days by sulphuric acid microdrops and 

thin films using a combination of AFM and XPS and observed the formation 

of pits and corrosion products. Solmaz and co-workers [21] examined 

the corrosion of mild steel by HCl solutions with and without the pres- 

ence of a corrosion inhibitory agent, using AFM to study changes in 

surface morphology in combination with a number of other techniques. 

When the surface was exposed to the HCl solution alone, corrosion pits 

were observed to form, which became both wider and deeper as the exposure 

time increased. When the surface was exposed to the HCl in combination 

with 10 mM 2-mercapto thiazoline, the surface was more uniform than 

surfaces exposed to HCl alone after 24 h exposure. For longer exposure 

times (approximately 120 h), a smoother surface was still evident when 

compared to treatment in the absence of 2-MT. A similar study by Qu et al. 

[22] examined the efficacy of a different additive (EDTA) on reduction of 

corrosion of steel surfaces by HCl. 

An interesting study was carried out by Valtiner et al. [23] into the effect 

of pH on acid dissolution of crystalline ZnO surfaces, which is often used 

as a protective coating for steels. It is the stability of the thin oxide covering 

that determines the corrosion resistance of zinc, and hence metal coated by 

it. The single crystalline surfaces were observed to consist of large flat sections 

several micrometres across, with step heights at the edges of 4–10 nm. 

When immersed in electrolytes of pH 11–5.5, no dissolution was observed. 

2.5

At pH 5.5, dissolution began to occur, but only at the step edges, not in the 

centre of the crystal planes. At pH values below this, as the pH decreased 

the dissolution rate increased, with a significant change in behaviour 

occurring below pH 4.0. Below this value, dissolution also began to occur 

at the flat crystal surfaces, although it was still most pronounced at the 

edges. It was suggested that this behaviour was due to the presence of 

oxygen in the step edges, which would be much more prone to attack by 

solution protons than the flat surfaces, which are positively charged at the 

higher pH values. 

A number of other studies have used AFM alongside other techniques 

to characterise a number of different coatings to protect metal surfaces 

from corrosion and wear, including TiN and ZrN thin films [24]; Sn–Ni 

and Sn–Cu alloy coatings [25, 26]; CrN films for enhanced wear resistance 

[27] and zirconia-based primers as coatings on aluminium [28]. 

4.8.3 biofilms at Metal Surfaces 

4.9 CONCLUsIONs 135 

Yu and colleagues [29] examined the difference between nano- and 

microcrystallization of stainless steel surfaces and the effect on the adhesion 

of biofilms. Using an AFM tip coated in a synthetic peptide to simulate 

a biofilm, adhesion measurements were made against nanocrystalline 

and microcrystalline surfaces. It was found that the measured adhesion 

in air was significantly reduced for the nanocrystalline surface compared 

with the microscrystalline surface. These observations were matched by 

similar results from the observations of attachment of whole bacterial 

cells to the same surfaces in bulk solution. 

4.9 COnCLUSIOnS 

The many benefits of AFM in investigations of membranes and membrane 

processes may be summarised as: 

1. Atomic force microscopy can determine the key properties of synthetic 

membranes: pore size distribution, surface morphology and 

surface roughness, surface electrical properties and surface adhesion. 

2. Correspondence between surface pore dimensions from AFM and 

MWCO is good. In addition, AFM gives surface pore size distribution. 

3. Operations in liquid and colloid probe techniques are particular 

advantages of AFM. 

4. AFM can establish the effects of changes in interactions over the surface 

of membranes, e.g. due to local morphology. 

5. AFM allows the visualisation of solute/membrane interactions. 

6. AFM is a very useful asset in assessing the properties of membranes 

during their development.


Indeed, it is apparent that the capabilities of AFM are very closely matched 

to the knowledge requirements of membrane scientists and engineers. 

In addition, AFM is a very useful technique for investigating the 

interaction of process streams with the materials of construction of process 

equipment, including studies of particle adhesion and the effects of 

corrosion. 

ACknOWLEDgEMEnTS 

We thank all who have contributed to this research, especially Teodora 

Doneva, Daniel Johnson, Bob Lovitt, Martin Peer, Peter Williams, Chris 

Wright and Huabing Yin. 

LIST OF AbbREVIATIOnS 

BSA bovine serum albumin 

EDTA ethylenediaminetetraacetic acid 

MF microfiltration 

MT mercapto thiazoline 

MWCO molecular weight cut-off 

NF nanofiltration 

PSU polysulphone 

RO reverse osmosis 

SPEEK sulphonated poly (ether ether) ketone 

UF ultrafiltration 

XPS X-ray photoelectron spectroscopy 

Names of membranes are manufacturers’ codes. 

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membrane by non-contact atomic force microscopy at single pore resolution, J. Memb. 

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Memb. Sci. 154 (1999) 205–212. 

[5] W.R. Bowen, T.A. Doneva, Atomic force microscopy characterisation of ultrafiltration 

membranes: correspondence between surface pore dimensions and molecular weight 

cut-off, Surf. Interface Anal. 29 (2000) 44–547. 

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J. Memb. Sci. 126 (1997) 77–89. 

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201 (2002) 73–83. 

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(2000) 63–172. 

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interactions on the rejection of colloids by membrane pores – visualisation 

and quantification, Chem. Eng. Sci. 54 (1999) 369–375. 

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ketone blend membranes: systematic synthesis and characterization, J. Memb. Sci. 181 

(2001) 253–263. 

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water with PSU/SPEEK blend UF/NF membranes, J. Memb. Sci. 206 (2002) 417–429. 

[12] K. Al-Anezi, D.J. Johnson, N. Hilal, An atomic force microscope study of calcium 

carbonate adhesion to desalination process equipment: effect of anti-scale agent, 

Desalination 220 (2008) 359–370. 

[13] W.R. Bowen, R.W. Lovitt, C.J. Wright, Atomic force microscope studies of stainless steel: 

surface morphology and colloidal particle adhesion, J. Mater. Sci. 36 (2001) 623–629. 


technique, interpretation and applications, Surf. Sci. Rep. 59 (2005) 1–152. 

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Condens. Matt. 15 (2003) L83–L87. 

[16] Y.I. Rabinovich, J.J. Adler, A. Ata, R.K. Singh, B.M. Moudgil, Adhesion between nanoscale 

rough surfaces. II. Measurement and comparison with theory, J. Colloid Interface 

Sci. 232 (2000) 17–24. 

[17] A. Abbott, G. Capper, K.J. McKenzie, A. Glidle, K.S. Ryder, Electropolishing of stainless 

steels in a choline chloride based ionic liquid: an electrochemical study with surface 

characterisation using SEM and atomic force microscopy, Phys. Chem. Chem. 

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[18] V. Vignal, J.C. Roux, S. Flandrois, A. Fevrier, Nanoscopic studies of stainless steel electropolishing, 

Corr. Sci. 42 (2000) 1041–1053. 

[19] J. Sanchez, J. Fullea, C. Andrade, J.J. Gaitero, A. Porro, AFM study of the early corrosion 

of a high strength steel in a diluted sodium chloride solution, Corr. Sci. 50 (2008) 

1820–1824. 

[20] R. Wang, An AFM and XPS study of corrosion caused by micro-liquid of dilute sulfuric 

acid on stainless steel, Appl. Surf. Sci. 227 (2004) 399–409. 

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inhibitive effect of 2-mercaptothiazoline on corrosion of mild steel in hydrochloric 

acid media, Electrochim. Acta 53 (2008) 5941–5992. 

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of cold rolled steel in the presence of benzotriazole in hydrochloric acid, 

Electrochim. Acta 52 (2007) 6811–6820.


[23] M. Valtiner, S. Borodin, G. Grundmeier, Stabilization and acidic dissolution mechanism 

of single-crystalline ZnO(0001) surfaces in electrolytes studied by in-situ AFM 

imaging and ex-situ LEED, Langmuir 24 (2008) 5350–5358. 

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arc technique, Appl. Surf. Sci. 253 (2006) 1683–1690. 

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properties of brush plated copper–tin alloys, Surf. Coat. Technol. 201 (2006) 

1145–1151. 

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alloy coating – an alternative for decorative chromium plating, J. Appl. Electrochem. 

37 (2007) 219–224. 

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of CrN films by ion beam enhanced deposition, Wear 217 (1998) 159–166. 

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Mezzi, R. Di Maggio, Zirconia primers for corrosion resistant coatings, Surf. Coat. 

Technol. 242 (2007) 5822–5888. 

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steel for reduced biofilm adherence, Nanotechnology 19 (2008) 335101.

C H A P T E R 

5 

AFM and Development 

of (Bio)Fouling-Resistant 

Membranes 

Nidal Hilal, W. Richard Bowen, 

Daniel Johnson and Huabing Yin 

O U T L I N E 


5.2 Measurement of Adhesion of Colloidal Particles and Cells 

to Membrane Surfaces 141 

5.3 Modification of Membranes 144 

5.3.1 Modification of Membranes with Quaternary Ammonium Salts 144 

5.3.2 Membrane Characterisation 145 

5.3.3 (Bio)Adhesion Forces between a BSA-Functionalised 

Colloid Probe and Membrane Surface 151 

5.4 Modification of Membranes with Sulphonated Poly 

(Ether-Ether Ketone) Polymers 163 





5.1 IntroduCtIon 

Pressure-driven membrane processes are widely used in water treatment 

applications. However, membrane fouling occurs due to the deposition 

of suspended particulates and dissolved materials on the membrane 



140 5. AFM AND DEvELOPMENT OF (BIO)FOULINg-REsIsTANT MEMBRANEs 

surface, restricting the efficiency of treatment processes which are dependent 

upon membrane filtration. Fouling becomes evident in the characteristic 

flux decline that results from increased resistance to flow due to 

the deposited material. Fouling analysis is difficult because the hydrodynamic 

aspects of concentration polarisation, as well as the physical 

chemistry of solute–solute and solute–membrane interactions must be 

considered. 

The formation of a fouling layer on the membrane surface, referred to 

as surface fouling, is the dominant fouling mechanism. Surface fouling 

involves the initial deposition of foulants of organic or inorganic origin 

on the membrane surface and the subsequent growth of a fouling layer 

that adversely influences membrane performance. 

Modification of the membrane surface can alter the surface chemistry 

and subsequently the surface charge properties of the membranes. The 

effectiveness of membranes significantly depends on their molecular and 

structural architecture, i.e. functional group distribution (2D or threedimensional 

[3D] distribution and uniformity), shielding of functional 

groups and their accessibility, and membrane morphology. Therefore, 

membranes containing different functional groups and characterised by 

different structural architectures are of special interest for the advance of 

their application in different areas. In their development, profound structure 

characterisation is of particular importance in providing an insight 

into the relationships between membrane performance and structure. 

Changes in surface morphology (roughness, pore size and pore size distribution 

[PSD]) and surface charge due to modification of membrane 

surfaces have been reported by several researchers [1–3]. 

The degree of hydrophobicity of both membrane and solutes determine 

the degree of fouling of membranes. It has been reported that 

protein fouling is greater for hydrophobic membranes than hydrophilic 

membranes [4]. However, the charge and hydrophobicity effects are 

functions of environmental conditions such as the salt concentration 

and the solution pH. The effect of charge decreases with increasing salt 

concentration due to a resultant decrease in the extent of the electrical 

double layer. 

Several authors have described natural organic matter (NOM) as 

one of the major membrane fouling agents in microfiltration, ultrafiltration 

and nanofiltration of surface water [5]. The chemical characteristics 

of the water in which the humic substances are dissolved, such as pH 

and ionic strength, are primary determinants in membrane fouling due 

to their effects on the conformational structure and charge of the humic 

substances. 

As bacterial surfaces contain proteins, polysaccharides and other 

biopolymers that can affect their adhesion to another surface, several

5.2 MEAsUREMENT OF ADHEsION OF COLLOIDAL PARTICLEs 141 

investigators have used different proteins to understand the role of biopolymers 

and their physiochemical properties in bacterial adhesion [6, 7]. 

In this chapter we will briefly summarise some of the literature pertaining 

to the adhesion of colloids and biocolloids to membrane surfaces 

as studied using AFM techniques. We will then concentrate on two more 

detailed examples in which the AFM has been used to characterise the 

physical and adhesive properties of membranes which have been developed 

specifically to reduce fouling. 

5.2 MEASurEMEnt of AdhESIon of ColloIdAl 

PArtIClES And CEllS to MEMbrAnE SurfACES 

The AFM has been used to measure adhesive forces between particles 

and various process surfaces. One important example is adhesion 

between particles, including both inorganic colloidal particles and bacterial 

cells, and filtration membranes. This interaction is of great importance 

when considering the fouling and biofouling of such surfaces. 

Particles adhere to the process membranes and reduce flow through the 

membrane, greatly reducing the filtration efficiency and working lifetime 

of the membranes. The process testing of new membranes is potentially 

expensive and time consuming. The quantification of adhesion forces 

between colloids and membranes can provide an important contribution 

to developing the theoretical prediction and optimisation and control 

of many engineering separation processes. As a result the development of 

AFM methods to quantify the adhesion of different materials to membranes 

of different compositions can potentially be very useful for membrane 

manufacturers and engineers [8]. When particle sizes are greater than the 

pore size in the absence of repulsive double layer interactions, such particles 

may plug the pores very effectively, leading to a catastrophic loss in 

filtration flux. 

Of the many established membrane characterisation techniques, only 

the colloid probe method can measure the adhesive forces between particles 

and membrane surfaces and hence allow prediction of the membrane 

fouling properties of the particles. In addition, the ability to make 

measurements in liquid allows the matching of observation conditions to 

those which occur in practice. The first demonstrations of the potential 

of the colloid probe technique to differentiate different membranes based 

upon the different adhesion properties was carried out by Brown and colleagues 

[8–12]. Two commercially available membranes with polymer 

molecular weights of 4 kDa were investigated. The first, ES 404, was made 

from a single polymer, polyethersulphone (PES). The second, XP 117, was 

made from a blend of different polymers created to have a potentially low


rate of membrane fouling. Measurements were made between polystyrene 

microspheres and these membranes in aqueous NaCl solutions at a 10 �2 M 

concentration and at a pH of 8.0. In Figure 5.1 plots of force normalised 

by the microsphere radius versus the displacement of the piezo in the 

direction normal to the membrane surface recorded whilst retracting the 

colloid probe away from the membrane surfaces are shown. At points A to 

A� the probe is in the region of constant compliance with the surface. For 

the region of the plot A� to B for the ES 404 membrane, a stretching of the 

probe and/or membrane occurs, due to the adhesive forces; the stretching 

continues at B to C, with adhesion force reducing as probe and membrane 

slowly separate, with final separation occurring at C. At C to D no 

net forces are acting between the probe and the surface, and this is taken as 

the point of zero force. The minimum force value (B) is taken as observed 

pull-off force F OFF and is a direct measure of the adhesive force. For the 

measurements presented in Figure 5.1, the values are 1.98 and 0.38 mN m �1 

for the ES 404 and XP 117 membranes, respectively – an approximately five- 

fold reduction. This demonstrates quantitatively that the membrane manufacturer 

has produced a membrane to which the test colloid attaches only 

weakly compared with a more conventional membrane. In other words the 

membrane is potentially low fouling in actual process applications. 

It is also worth noting that the adhesive interaction between the probe 

and the ES 404 membrane took place over a distance of approximately 

400 nm, most likely due to the stretching of the probe and/or the membrane 

surface. When the adhesion of a ‘cell probe’ (Figure 5.2) created 

F/R (mNm –1 ) 

5 

4 

3 

2 

1 

0 

–1 

ES 404 membrane 

XP 117 membrane 

D C 

–2 

B 

–3 

1000 1200 1400 1600 1800 2000 

Piezo displacement (nm) 

fIgurE 5.1 Normalised retraction force versus displacement for a polystyrene colloid 

probe and two filtration membrane at pH 8.0, 10 �2 M NaCl. Adhesion against the XP 117 

membrane formulated for low fouling is much reduced compared with the more conventional 

ES 404 membrane. 

Aʹ 

A

5.2 MEAsUREMENT OF ADHEsION OF COLLOIDAL PARTICLEs 143 

with a single yeast cell to a silica surface was undertaken, the adhesive 

interaction also took place over a large distance [12], again most 

likely representing the stretching of the probe. Conversely, in studying 

the adhesion between systems of hard inorganic surfaces, the adhesive 

interactions take place over very short distances of the order of no more 

than a few nanometres [13–15]. This is a consideration for manufacturers 

of membranes when studying a heterogeneous range of materials. This 

behaviour is also of note for general colloid probe interactions. The deformation 

of soft surfaces in close proximity due to long-range and mechanical 

forces when in contact makes the determination of the actual surface 

separation and assignment of the point of zero distance problematic. For 

this reason many researchers plot only the displacement of the piezo, 

rather than the actual surface separation. This topic is discussed in more 

detail elsewhere in this book. 

Protein-coated colloid probes were used to compare the adhesive 

forces between silica colloids and bovine serum albumin (BSA)-coated 

silica spheres with the same membranes as described earlier [10]. BSAcoated 

silica probes demonstrated significant adhesion with both types 

of membranes, compared to silica probes, which had no measurable 

adhesion. The development of the colloid probe technique for the AFM 

as a sensor for quantifying the adhesive forces at membrane surfaces 

provides a relatively fast procedure for assessing the potential fouling of 

membrane surfaces by particles of different materials. In addition only 

fIgurE 5.2 SEM image of a yeast cell attached to the apex of an AFM microcantilever 

to create a ‘cell probe’.


small pieces of membrane are necessary for experiments to be undertaken. 

Ultimately the direct measurements of the AFM will help to assist 

in the development of new membranes with more fouling-resistant properties. 

(Further information on ES 404 and XP 117 is given in Chapter 4.) 

5.3 ModIfICAtIon of MEMbrAnES 

The development of high-performance membranes involves the 

selection of a suitable material and the formation of this material into a 

desired membrane structure. However, it is often necessary to modify the 

membrane material or the structure to enhance the overall performance 

of the membrane. The field of membrane technology is extremely broad, 

and the applicability of surface modification for different types of membranes 

is equally diverse. Polymeric membranes of nearly every variety 

have been utilised in the literature as substrate for polymer modification 

by the addition of another polymer. 

There are many techniques for the attachment of polymers to membrane 

surfaces. Some of these techniques, such as electrochemical and 

�-irradiation, require continuous application of current or radiation 

throughout the polymerisation process. Others, such as UV-initiation, 

electron beam deposition, plasma treatment and silanisation, create reactive 

sites for subsequent formation of the polymer in situ, in general by 

free radical polymerisation. Whole macromolecules can be incorporated 

either by their cross-linking within the pores or by specific attachment of 

polymer chains to the membrane pore surfaces. Such modification methods 

are commonly applied to improve various membrane properties, 

including improvement of their surface-fouling resistance. Rendering the 

membrane surface more hydrophilic is a widely used method to reduce 

their tendency to become fouled. 

Modification by photo-initiated graft polymerisation with various 

hydrophilic monomers has been extensively applied to vary the hydrophilicity 

of the membrane surface. Acrylic acid, hydroxyethyl methacrylate 

(HEMA), poly(ethylene glycol) derivatives and vinyl pyrolidinone are 

examples of such hydrophilic monomers. Improvement in membrane fouling 

tendency has been reached after modification with such hydrophilic 

monomers [16–18]. 

5.3.1 Modification of Membranes with Quaternary 

Ammonium Salts 

Quaternary 2-dimethyl-aminoethylmethacrylate (qDMAEMA) was 

chosen for the modification of PES and polyvinylidene fluoride (PVDF) 

membranes using photo-initiated graft copolymerisation method [1, 19, 20].

The antibacterial activity of initial unmodified (PES and PVDF) membranes 

as well as membranes modified with qDMAEMA polycations 

were evaluated against E. coli bacteria. After incubation with viable E. coli 

bacterial cells on each membrane, the growths of bacterial plaques were 

compared. Figure 5.3 shows PES membranes of which one is modified by 

incubation with 367 �g cm �2 qDMAEMA. The results showed that membrane 

samples with grafted qDMAEMA as well as ones modified with PEI 

possess a strong antimicrobial action towards E.coli bacteria. 

This antimicrobial activity was found to be independent with relation 

to the degree of modification (DM) of the membrane. The modified membranes 

possessing biocide properties could be potentially more resistant 

to (bio)fouling in water treatment applications. 

5.3.2 Membrane Characterisation 

5.3 MODIFICATION OF MEMBRANEs 145 

Membrane Surface Morphology 

Membrane surface topography and conformational changes due 

to modification were examined using AFM in contact mode. All AFM 

images were made in air at room temperature. Figure 5.4 presents 3D 

AFM images of initial PES membranes and modified membranes with 

different degrees of polymer grafting [8, 20]. 

It can be seen that surface topography is markedly different in texture 

for unmodified membranes compared with the modified membranes, 

(a) (b) 

fIgurE 5.3 Viability of E.coli cells on the surface of initial PES (a) and modified 

with qDMAEMA membranes, DM � 367 �g cm �2 (b). Five millilitres of E. coli suspension 

(15 E. coli per ml) were filtered through both membranes.


25 µm 

12.5 µm 12.5 µm 

0 µm Z scale = 720 nm 

(a) (c) 

12.5 µm 

25 µm 

12.5 µm 

although both are characterised by the same nominal pore size. The surface 

of grafted membrane having the lowest DM (shortest polymer chain length) 

appeared to have a laterally inhomogeneous structure consisting of clusters. 

As the DM increased (leading to an increased graft chain length), the clusters 

became higher and the grafted chain gathered into larger clusters. 

Membrane Surface Analysis 

From AFM images, surface analysis was carried out using instrument 

software to obtain surface roughness parameters. The formation of 

the graft polymer layer on the membrane surface resulted in significant 

changes in surface morphology. Structural modifications become more 

pronounced with increasing DM. Figure 5.4 and Tables 5.1 and 5.2 present 

quantitative characteristics of the surface morphology of the initial 

and modified membranes derived from the AFM images [20]. 

The same trend can be observed in the roughness values for both 

PES and PVDF membranes. A slight increase in the membrane roughness 

compared with the unmodified membrane was observed for membranes 

modified with the lowest degree of grafted polymer (202 �g cm �2 ). 

At such a DM, grafted chains could be accommodated within the pores. 

Further increases in DM led to a significant increase in surface roughness 

with a layer of grafted polymer forming its own porous structure. 

0 µm 

25 µm 

Z scale = 720 nm 

25 µm 

0 µm Z scale = 720 nm 0 µm Z scale = 720 nm 

(b) (d) 

fIgurE 5.4 High-resolution 3D AFM images of initial (a) and modified with 

qDMAEMA (b)–(d) PES membranes; (b) DM � 202 �g cm �2 , (c) DM � 367 �g cm �2 and (d) 

DM � 510 �g cm �2 .


tAblE 5.1 AFM Measurements of surface Morphology of Initial and 

Modified PEs Membranes with qDMAEMA. 

DM (�g cm �2 ) Ra (nm) rms (nm) 

Average 

Height (nm) 

Pore Size and Pore Size Distribution 

Pore size and PSD of each membrane were determined from AFMdetermined 

topography. The lognormal distribution was chosen to represent 

the pore size data for each of the membranes. This was found to give 

a good fit to the PSD. All of these distributions were fitted to lognormal 

distributions given by frequencies (%f ): 

1 dp 

% f � % fmax exp � ln 

2 X 2 

⎡ 

2 

⎛ ⎞ ⎤ 

⎢ ⎜ ⎥ 

⎢ ⎜ 

⎢ � ⎝⎜ 

0 ⎠⎟ 

⎥ 

⎣ 

⎦ 

Maximum 

Range (nm) 

0 27.93 36.43 161.77 275.46 

202 32.26 42.91 250.09 378.4 

367 67.37 85.28 329.46 537.27 

tAblE 5.2 AFM Measurements of surface Morphology of Initial and 

Modified PvDF Membranes with qDMAEMA. 

DM (�g cm �2 ) Ra (nm) rms (nm) 

Average 

Height (nm) 

Maximum 

Range (nm) 

0 91.52 114.38 402.07 699.97 

224 92.91 116.04 406.18 701.43 

346 101.68 127.42 433.97 834.53 

(5.1) 

where d p is the measured pore size, � the standard deviation of the measurements, 

%f max the maximum frequency and � 0 the modal value of d p. 

Mean pore sizes and PSDs of initial membranes determined from 

AFM images are shown in Table 5.3. This table shows that with a mean 

pore size of 0.535 � 0.082 �m, the PVDF membrane has slightly larger 

pores than the PES membrane (mean pore size 0.470 � 0.188 �m). PSDs 

are detailed in Figure 5.3, along with fits described by equation (5.1). The 

measured pore sizes are larger than the nominal pore size of 0.22 �m as 

specified by the manufacturers. The AFM data confirm that the pore


sizes of studied membranes are of approximately the same size. The 

topographical images give a clear perception of a notable difference in 

the surface morphology of the membranes used for the modification. 

A quantification of the surface parameters (Table 5.3) provides an insight 

into morphological particularities of these membranes which influence 

both the membrane separating properties and the process of modification 

by graft copolymerisation. 

The two membranes under study have notably different PSDs. It 

can be noted here that PVDF has a narrower PSD with pore sizes from 

0.336 to 0.68 �m compared with a PSD ranging from 0.219 to 0.948 �m in 

PES membranes. Moreover, these membranes significantly differ in surface 

roughness, with the PES membrane being smoother than the PVDF 

membrane. Regarding the AFM images, one might notice that the 

smoother surface allows for better contrast in pore observation, but more 

importantly the surface roughness is expected to have an influence on 

the graft copolymerisation. 

The rate of membrane modification was higher in the case of PES 

membrane than PVDF membrane [19]. It is impossible to associate the 

difference only with the contribution of surface morphology. It is well 

known that polysulphone and PES are intrinsically photo-active, undergoing 

bond cleavage with UV irradiation to produce free radicals even 

without the use of photo-initiators. PVDF is less photo-reactive than 

PES and produces less surface free radicals than PES. However, higher 

density of free radicals at the surface of more photo-reactive PES membranes 

also results in a higher probability of termination of chain growth 

and formation of cross-linked structures. These processes restricting an 

increase in the DM are competitive with respect to the chain growth. 

Since competitive processes, which enhance and decrease the amount of 

grafted polymer, occur simultaneously in the case of the photo-reactive 

polymer, the influence of surface morphology on graft copolymerisation 

should not be discarded. For the relatively rough surfaces, such as 

PVDF membrane, the decrease in UV-irradiation effectiveness and steric 

hindrance for polymer growth in narrow valleys are possible effects that 

may decrease the modification to some degree. 

tAblE 5.3 Parameters of Pore size and PsD Obtained from AFM Images for Initial 

PEs and PvDF Membranes. 

Pore size (�m) PSD parameters 

Membrane Mean Minimum Maximum X 0 (�m) %f max � 

PES 0.470 � 0.188 0.219 0.948 0.353 � 0.028 19.8 � 2.2 0.56 � 0.08


Before detailed discussion of the quantitative characteristics of surface 

morphology, it is worth noting that the chosen lognormal pattern for 

PDS described by equation (5.1) gave a correlation coefficient of at least 

0.95 for all fitted curves. The most probable pore sizes estimated from 

fitted curves were very close to the mean pore diameter calculated from 

corresponding sets of pore sizes for the initial and modified membranes 

(Tables 5.4 and 5.5). 

According to Figure 5.5(a), the initial PES membrane has a very wide 

PSD with a � value of 0.56 �m. However, grafting of poly-qDMAEMA 

resulted in narrowing of the PSD and shifting the whole curve towards 

smaller pore sizes. As a result, mean pore size is gradually decreasing 

with the increase in the amount of poly-qDMAEMA grafted to the membrane 

surface. Significant improvement of the PSD was observed even 

for the modified PES membranes with the smallest DM (Table 5.4). 

Narrowing of the PSD occurred mostly due to the disappearance of 

large pores (larger than 0.6 �m). Taking into consideration that substantial 

narrowing of large pores demands higher quantities of grafted polymer 

tAblE 5.4 AFM Measurements of Pore size and PsD of Initial and 

Modified PEs Membranes with qDMAEMA. 

Mean pore PSD parameters 

DM (�g/cm 2 ) size (�m) X 0 (�m) %f max � 

0 0.470 � 0.188 0.353 � 0.028 19.8 � 2.2 0.56 � 0.08 

202 0.337 � 0.098 0.278 � 0.010 41.4 � 4.4 0.32 � 0.04 

367 0.293 � 0.072 0.281 � 0.003 51.3 � 2.0 0.26 � 0.01 

510 0.100 � 0.083 0.075 � 0.004 26.9 � 2.9 0.40 � 0.05 

tAblE 5.5 AFM Measurements of Pore size and PsD of Initial 

and Modified PvDF Membranes with qDMAEMA. 

Mean pore PSD parameters 

DM (�g/cm 2 ) size (�m) X 0 (�m) %f max � 

0 0.535 � 0.082 0.555 � 0.003 51.2 � 1.7 0.14 � 0.01 

224 0.445 � 0.083 0.439 � 0.018 35.1 � 4.1 0.28 � 0.02 

346 0.334 � 0.079 0.297 � 0.013 44.3 � 5.7 0.30 � 0.01


Pore density % 

25 

20 

15 

10 

5 

0 

0 

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 

(a) Pore size (µm) 

(c) 

Pore size (µm) 


40 

30 

20 

10 

AFM data 

Fitted data 

AFM data 

Fitted data 

compared to smaller pores, it can be assumed that higher rates of polymer 

growth initiated at the walls of larger pores. As mentioned earlier, 

at the entrance of narrower pores, higher density of free radicals results 

in chain termination and consequently lower rate of polymer grafting. 

With time, when the PSD becomes more uniform, free radicals are eventually 

distributed across the membrane surface. This leads to a gradual 

decrease of all surface pores with PSD shifting to smaller sizes. With DM 

higher than 202 �m cm �2 , slight fluctuation in the width of PSD (�) was 

observed. 

It can be seen from Table 5.5 that similar behaviour is observed regarding 

changes in the surface morphology of the PVDF membrane as for the 

PES membrane. However, the unmodified PVDF membrane has a more 

uniform PSD than the PES membrane. With a mean pore size approximately 

0.54 �m, PSD of this membrane is characterised by a low value 

of �, �0.14 �m, compared with �0.56 �m for PES membranes. Although 

modification of PVDF membrane with grafted qDMAEMA also led to 

PSD shifting towards lower pore sizes, PSD was wider for the modified 

membranes compared with initial membrane. 



50 

40 

30 

20 

10 

30 

25 

20 

15 

10 

5 

AFM data 

Fitted data 

AFM data 

Fitted data 

0 

0 

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 

(b) 


(d) 


fIgurE 5.5 PSDs of initial (a) and modified with qDMAEMA (b)–(d) PES membranes; 

(b) DM � 202 �g cm �2 , (c) DM � 367 �g cm �2 and (d) DM � 510 �g cm �2 .

Force (nN m –1 ) 

Loading force 

(mN m –1 ) 

52 

55 

61 


Separation (nm) 

fIgurE 5.6 Representative approach (grey) and retraction (black) force curves of 

BSA-modified colloid probe to grafted membrane with qDMAEMA at different loading 

forces (pH 7). 

5.3.3 (bio)Adhesion forces between a bSA-functionalised 

Colloid Probe and Membrane Surface 

Adhesion force measurements were performed using the colloid probe 

technique. Colloid probes were prepared by immobilising modified 

microsphere with BSA to a tipless ultralever silicon cantilever. 

Examples of retraction curves measured at three different loading 

forces for a BSA-modified microsphere interacting with a PES membrane 

grafted with qDMAEMA, shown in Figure 5.6, demonstrate that the adhesion 

force (pull-off force) increases with the force applied via the colloid 

[20]. Similar findings have been observed in previous studies [7, 14]. The 

increase in the adhesion force is most likely to result from an increase in 

the number of chemical bonds formed between the biopolymers when the


surfaces are forced into closer contact using higher loading forces [7]. In 

addition the deformation of the membrane surface at high loading forces 

may increase the area of contact between the probe and the membrane 

surfaces. In order to exclude the influence of loading force in comparison 

of interactions force, the experimental results are presented by plotting the 

adhesion force versus the loading force. For the purpose of comparison, 

the adhesion force at loading force equal to 80 mN m �1 was measured, 

interpolated or extrapolated from the obtained experimental data. 

Interactions Forces between Initial Membranes and Functionalised 

Colloid Probes 

Effect of pH on Measured Adhesion Figure 5.7 shows the normalised 

adhesion force measurements versus the normalised loading force applied 

to the cantilever between a BSA-modified probe and initial PES membrane 

at different pH values. It can be seen that the adhesive force is highest at 

pH 5, followed by moderate values at pH 3 and the lowest at pH 7. 

First, at pH 7 both the BSA and the membrane surface are negatively 

charged [21], which provoke increases in the repulsive electrostatic interaction, 

leading to a reduction in adhesion. BSA is more hydrophobic at 

pH 5 than 7, which would be expected to increase adhesion. Secondly, the 

Adhesion force (mN m –1 ) 

12 

10 

8 

6 

4 

2 

pH=3 

pH=5 

pH=7 

Loading force (mN m –1 0 

40 60 80 100 120 140 

) 

fIgurE 5.7 Relationship of adhesion and loading forces between initial PES and BSA 

probe in different pH solution. The dotted line is an extrapolated line.


protein has a more expanded structure at pH values away from its isoelectric 

point (pI) of 4.8 [22]. Thus a steric repulsive interaction between 

the interacting surfaces will be higher at pH 3 than at pH 5, leading to 

reduced adhesion at pH 3. Finally, PES possesses a slight positive charge 

at pH 3 [21], provoking an electrostatic repulsive force. 

A linear relationship between adhesion and loading forces for interactions 

between BSA-modified probe and initial PVDF membrane at different 

pH is shown in Figure 5.8. A similar trend is observed to the initial 

PES membrane, with the adhesive force having the highest value at pH 5, 

whereas the lowest adhesion force was measured obtained at pH 7. 

The PVDF membrane possesses a negative charge in the pH range 

studied with its magnitude increasing with increased pH [23]. This 

explains the lower adhesion force between the BSA-modified probe 

and PVDF surface at pH 7 where both surfaces carry a negative charge. 

Increases in steric repulsion at pH 3 and in BSA hydrophobicity at pH 5 

resulted in higher adhesion at pH 5. 

Effect of Ionic Strength on Adhesion Forces The effect of ionic concentration 

on adhesion force is shown in Figure 5.9. Increased NaCl concentration 

led to an increase in the adhesion force between the BSA probe and the PES 


14 

12 

10 

8 

6 

4 

pH=3 

pH=5 

pH=7 


40 60 80 100 120 140 160 180 200 

) 

fIgurE 5.8 Relationship of adhesion and loading forces between initial PVDF and BSA 

probe in different pH solutions.



25 

20 

15 

10 

5 

1 mM NaCl 

10 mM NaCl 

100 mM NaCl 


60 80 100 

) 

120 

fIgurE 5.9 Relationship of adhesion and loading forces between initial PES and BSA 

probe in different ionic strength solution at pH � 5.8. The dotted line is an extrapolated line. 

membrane surface. The adhesion of the BSA probe to the initial unmodified 

PES increased by a factor of �2.4 across the concentration range 1–100 mM 

NaCl. This behaviour is qualitatively consistent with DLVO theory [24], as 

increasing the ionic strength compresses the thickness of the electrostatic 

double layer and should therefore reduce the repulsion force between the 

two surfaces, resulting in an increase in measured adhesion force. 

The adhesion force measured between a BSA-coated probe and 

PVDF membrane surface at different ionic strength values is shown in 

Figure 5.10. As with the PES membrane, an increase in ionic strength 

led to an increase in the observed adhesion force. The adhesion force 

increased by a factor of 1.7 across the dissolved NaCl range of 1–100 mM. 

This is due to charge screening effects at higher ionic concentrations 

reducing the electrostatic repulsion, hence increasing the adhesion force 

between the interacting surfaces. 

Comparison of (Bio)Adhesion Force Measurements between PES 

and PVDF Initial Membranes 

Figure 5.11 shows the adhesion force for unmodified PES and PVDF 

membranes measured using BSA-coated colloid probes in solution at different 

pH values. A similar trend was observed for the adhesion force as 

a function of pH for both membranes. However, the PVDF membrane


10 

8 

6 

4 

2 


0 

40 60 80 100 120 140 160 

Loading force (mN m –1 ) 

1 mM NaCl 

10 mM NaCl 

100 mM NaCl 

fIgurE 5.10 Relationship of adhesion and loading forces between initial PVDF and 

BSA probe in different ionic strength solutions at pH � 5.8. 


10 

8 

6 

4 

2 

0 

1 2 3 4 5 6 7 8 9 

pH 

PES 

PVDF 

fIgurE 5.11 Comparison of adhesion forces of BSA-modified probe to unmodified 

PES and PVDF membranes in various pH solutions.


showed a lower adhesion force than PES. This is most likely due to the 

PES membranes having a higher degree of hydrophobicity compared 

with PVDF. In addition, the PVDF membrane has a higher �-potential 

than the PES membrane [21, 23]. Thus a higher repulsive electrostatic 

force would be expected between the probe and the unmodified PVDF 

membrane than unmodified PES membrane. 

Effect of Ionic Strength A comparison of the adhesion force for both 

membranes as a function of ionic concentration is shown in Figure 5.12. 

In general a higher adhesion force is observed for PES membrane than 

PVDF membrane over the studied ionic strength range, except at ionic 

strength of 1 mM NaCl where adhesion force was small and no significant 

difference in adhesion of both membrane types is observed. At the 

highest ionic strength, the difference is the most dramatic. PES membrane 

is more hydrophobic than PVDF membrane. As a result a hydrophobic 

attractive force leads to higher adhesion force for PES membrane 

than PVDF membrane. 

Interactions Forces between Membranes Modified with qDMAEMA 

and BSA-Functionalised Colloid Probe 

Effect of pH The effect of solution pH on adhesion force for PES membranes 

modified with qDMAEMA is shown in Figure 5.13. An increase in 

adhesion force with increasing pH was observed for modified membranes 

with three different DMs and is approximately threefold at a loading force 

of 80 mN m �1 . 

The dominant contribution in the increase in adhesion force with increasing 

pH can be attributed to the electrostatic force between the positively 

charged modified membranes and the BSA probe. At pH 3 both surfaces 

(membrane and BSA probe) possess a positive charge resulting in greater 

repulsion at this pH and hence a lower adhesion than seen for other pH 

values. At pH 7 the modified PES membranes remains positively charged, 

whereas BSA carries a negative charge. This change in the nature of the 

electrostatic interaction leads to a greater observed adhesive force at pH 7. 

Figure 5.14 shows the results for the effect of pH on the measured adhesion 

force of BSA to PVDF membrane functionalised with qDMAEMA. 

An increase in adhesion force with increasing solution pH was again 

observed. The experimental results for PVDF grafted with different DMs 

reveal the same trend. Taking into consideration the amphoteric behaviour 

of BSA, which leads to a change in protein charge with changing 

pH, the BSA possesses a positive charge at pH values below the pI and 

a negative charge at pH values above the isoelectric point. This explains 

the relatively high adhesion at pH 7 where both the BSA and the membrane 

surface are oppositely charged. Thus, an attractive electrostatic force 

between the interacting surfaces results in higher adhesion.


20 

15 

10 

5 


0 

0.1 1 10 100 

Ionic strength (mM) 

PES 

PVDF 

fIgurE 5.12 Comparison of adhesion forces of BSA-modified probe to initial PES and 

PVDF membranes in various ionic strength solutions. 


8 

7 

6 

5 

4 

3 

2 

1 

20 40 60 80 100 120 140 


pH=3 

pH=5 

pH=7 

fIgurE 5.13 Relationship of adhesion and loading forces between BSA probe and PES 

membrane modified with qDMAEMA (DM � 510 �g cm �2 ) at different pH solution. The 

dotted line is an extrapolated line.



3.5 

3.0 

2.5 

2.0 

1.5 

1.0 

0.5 

Loading force (mN m –1 0.0 

60 70 80 

) 

90 

pH=3 

pH=5 

pH=7 

fIgurE 5.14 Relationship of adhesion and loading forces between BSA probe and 

PVDF membrane modified with qDMAEMA (DM � 530 �g cm �2 ) in different pH solution. 

Steric interaction could be another factor which plays a role in reducing 

the adhesion force observed with both membranes at pH 3. The overlap 

of the expanded protein layer and the modification of polymer chain 

of qDMAEMA, which is fully dissociated at this pH, enhance the repulsive 

interactions between the colloid probe and the surface of the modified membrane. 

In addition, at pH 5 there is practically no electrostatic interaction 

because this pH is close to the isoelectric point of the protein (the net charge 

is around zero) and, therefore, the electrostatic repulsion is negligible. As 

at pH 5 the protein has no net charge and so the structure of the protein is 

more compact and it has hydrophobic properties, such interaction may lead 

to high adhesion at pH 5 than at pH 3. 

Effect of Ionic Strength Normalised adhesion forces versus normalised 

loading forces for interactions involving the modified PES membrane are 

shown in Figure 5.15 at different solution ionic strengths. An increase in 

adhesion force with increased ionic strength is evident. 

The normalised adhesion force measured between BSA versus PVDFmodified 

membrane with qDMAEMA was examined as a function of 

ionic strength by varying the NaCl concentration (Figure 5.16). The 

adhesion force was also found to increase with increasing solution ionic 

strength. This is due to the compression of the double layer, which leads 

to the increase in adhesion force with increasing ionic strength.


10 

8 

6 

4 

2 


1 mM NaCl 

10 mM NaCl 

100 mM NaCl 


0 20 40 60 80 100 120 

) 


modified membrane with qDMAEMA (DM � 510 �g cm �2 ) in different ionic strength solutions 

at pH � 5.8. The dashed line is an extrapolated line. 

Comparison of (Bio)Adhesion Force Measurements Between 

Unmodified Membranes and Membranes Modified with qDMAEMA 

Effect of pH The normalised adhesion forces at the same loading force 

(loading force � 80 mN m �1 ) for initial and modified PES membranes 

with qDMAEMA are shown in Figure 5.17. It is clear that the unmodified 

membrane has a higher adhesion force than the modified membranes at 

pH 3 and 5, whereas the lowest adhesion was observed at pH 7. In addition, 

at pH 3 modified membrane with the lowest DM exhibits the lowest 

adhesion. At pH 5 modified membrane with DM of 510 �g cm �2 showed 

the lowest adhesion force whereas both membranes show almost the 

same adhesion at pH 7. 

The BSA-functionalised probe and both modified and unmodified 

membranes all possess a positive surface charge at pH 3. However, the 

qDMAEMA-functionalised membrane possesses a markedly greater 

charge than the unmodified PES membrane. The resulting greater electrostatic 

repulsion accounts for the greater adhesive forces observed with 

the initial unmodified PES membrane than with the modified membrane. 

When the surrounding solution is at pH 7, both the initial PES membrane 

and the BSA possess negative surface charges, with the qDMAEMA 

membrane still carrying a positive charge. This accounts for the modified 

membrane having a greater adhesive force with the BSA-coated probe 

than the unmodified membrane.



7 

6 

5 

4 

3 

2 

1 

0 

40 60 80 100 120 140 


1 mM NaCl 

10 mM NaCl 

100 mM NaCl 


PVDF membrane modified with qDMAEMA (DM � 530 �g cm �2 ) in different ionic strength 

solutions at pH � 5.8. 


12 

10 

8 

6 

4 

2 

0 

1 2 3 4 5 6 7 8 9 

pH 

Initial PES 

Modified PES DM = 202 μg cm –2 



fIgurE 5.17 Comparison of adhesion forces of BSA-modified probe to initial and 

modified with qDMAEMA membranes in various pH solutions.


Figure 5.18 shows the adhesion forces between initial and modified 

PVDF membranes and the BSA-functionalised probe. At pH 3 and 5 the 

initial PVDF membrane showed a higher adhesion than the modified 

PVDF membrane. At the highest pH at which measurements were made, 

the adhesion for the unmodified membrane was lower than for the modified 

membranes, except for the membrane with the highest DM. 

Effect of Ionic Strength The adhesion force measured between BSAcoated 

colloid and modified PES membranes is shown in Figure 5.19. The 

adhesion force for all the investigated membranes was found to increase 

with increasing solution ionic strength. The modified membrane with 

DM 367 �g cm �2 demonstrated the lowest adhesion force followed by the 

initial membrane, which shows an increase in adhesion force compared 

to modified membrane with medium DM. 

Figure 5.20 shows the adhesion results for initial and grafted PVDF 

membranes using BSA probes at different solution ionic strengths. An 

increase in adhesion force with increasing ionic strength was observed 

for both unmodified and modified membranes. Again a similar result to 

PES membranes is noticed here where adhesion force has its lowest value 

for modified PVDF with DM 346 �g cm �2 except at ionic strength of 1 mM 

NaCl whereas grafted membrane with DM 530 �g cm �2 shows a slightly 

lower adhesion than modified with DM 346 �g cm �2 . 


12 

10 

8 

6 

4 

2 

Initial PVDF 

Modified PVDF DM = 224 μg cm –2 



0 

1 2 3 4 5 

pH 

6 7 8 9 


modified with qDMAEMA membranes in various pH solutions.



60 

50 

40 

30 

20 

10 

Initial PES 




0 

0.1 1 10 


100 


modified with qDMAEMA membranes in solutions of increasing NaCl concentration. 


12 

10 

8 

6 

4 

2 

0 

0.1 1 10 100 


Initial PVDF 





modified with qDMAEMA membranes in various ionic strength solutions.

5.4 MODIFICATION OF MEMBRANEs wITH sULPHONATED 163 

The lower adhesion for modified PVDF membranes compared to the 

initial PVDF especially at DM 348 �g cm �2 suggests that the hydrophobic 

interactions are playing the dominant role where the higher hydrophobicity 

of initial membranes results in increasing its adhesion compared to 

modified membranes. 

5.4 ModIfICAtIon of MEMbrAnES wIth 

SulPhonAtEd Poly(EthEr-EthEr KEtonE) PolyMErS 

One of the most widely used materials in the manufacture of filtration 

membranes is polysulphone, due to its excellent mechanical, thermal and 

chemical stability. Unfortunately a high degree of hydrophobicity possessed 

by unmodified polysulphone membranes renders them prone to 

fouling by a wide range of solutes. To improve membrane effectiveness by 

reducing fouling, and particularly biofouling, hydrophilic polymers may 

be incorporated into membranes or the membranes modified by the addition 

of extra functional groups by, for instance, sulphonation. The addition 

of charge bearing groups to the membrane surface will not only decrease 

the degree of hydrophobicity of the membrane but can also cause increased 

rejection of particles and solutes of identical charge [25]. 

Poly(ether-ether ketone) (PEEK or poly(oxy-1,4-phenyleneoxy-1,4- 

phenylcarbonyl-1,4-phenylene) is a very chemically stable polymer, 

soluble only in strong acids. This includes concentrated sulphuric or 

chlorsulphonic acid, which yields a sulphonated PEEK (SPEEK) [26, 27]. 

Studies of solubility of SPEEK suggest that it is more hydrophilic than 

merely sulphonated polysulphone [28]. 

Studies have been carried out to investigate the effectiveness of using 

SPEEK as a charged polymer additive to polysulphone membranes to 

not only reduce fouling by the introduction of charged groups, but also 

as a pore-forming agent due to its hydrophilicity [29, 30]. In particular 

here we will report the use of AFM in the characterisation of the effects 

of the SPEEK additives on surface morphology and fouling resistance. 

All membranes were characterised using AFM-obtained topographies. 

In Figure 5.21 example images of a plain polysulphone membrane and 

a membrane of polysulphone blended with 5% SPEEK are shown. Data 

obtained from AFM images, including average pore size (r p), root mean 

square (rms) roughness and surface porosity, are summarised in Table 5.6. 

Little variation is seen in rms roughness, although there is a trend for 

decreasing roughness with higher SPEEK content. Porosity variation 

follows a similar trend to that calculated from permeability of the membrane 

to water [29], but of a much smaller magnitude, suggesting that the 

increase in water permeability as SPEEK content increases is only partly


300 

(a) 

Å 

2.00 

1.00 

0.00 

200 

Å 

100 

0 0 

100 

Å 

200 

300 

Å 

4.00 

3.00 

2.00 

1.00 

0.00 

200 

Å 

100 100 

due to increase in the surface porosity. Changes in the thickness and/or 

the structure of the porous layer of the membrane may account for this. 

Force measurements were also carried out between �4-�m silica 

spheres and membranes. Figure 5.22 shows examples of typical data for 

force measurements taken from polysulphone membranes, with and without 

SPEEK present in 0.01 M NaCl. For the non-SPEEK membrane (P-P) the 

colloid probe snaps-in to the membrane surface, which indicates the presence 

of long-range attractive forces, sufficient in magnitude to overcome 

the restoring force on the cantilever. This type of attraction leads to fouling 

300 

0 0 

fIgurE 5.21 AFM images of polysulphone membranes obtained with contact mode in 

air. (a) Polysulphone membrane and (b) polysulphone/SPEEK membrane (5% SPEEK prepared 

at 20°C). Roughness values were obtained from 2 � 2 �m images. 

tAblE 5.6 summary of AFM Characterisation Data for sPEEK Modified 

Polysulfone Membranes. 

(b) 

P-P S0.5-20 S2-20 S5-20 S2-10 S2-60 

r p (nm) 0.93 � 0.15 0.89 � 0.22 0.93 � 0.15 0.73 � 0.18 1.05 � 0.22 0.86 � 0.26 

rms roughness 

(nm) 

3.2 4.2 3.5 2.5 3.1 2.1 

Porosity, e (%) 6.0 9.0 14.1 16.9 15.1 12.8 

Snap-in events 

(out of 9) 

F off, F/R 

(mN/m) 

9 4 3 0 1 4 

28.5 � 4.3 10.0 � 14.8 3.9 � 1.6 0.75 � 2.7 � 2.8 9.6 � 5.3 

Å 

200 

300


FIR/mN m –1 

(a) 

FIR/mN m –1 

(b) 

2 

1 

0 

–1 

5 

0 

–5 

–10 

–15 

–20 

–25 

–30 

0 20 40 60 

Distance/nm 

–2 

0 

Approach 

Retraction 

20 

Distance/nm 

Approach 

Retraction 

fIgurE 5.22 Example normalised force versus distance curves against (a) P-P type 

membrane and (b) S5-20 membrane. 

of the membrane. When the probe is retracted away from the membrane 

surface, a large attractive force is again measured. The difference between 

the attractive force at its greatest magnitude and the force measured when 

the probe has no net forces acting upon it (its free level) is the measured 

adhesion force, F off. In contrast, for the S5-20 SPEEK membrane, no snapin 

is observed. This is most likely due to the silica probe and membrane 

surface carrying charges which are identical in sign. When the particle 

is retracted, only a moderate adhesive force was measured. Data for the 

40 

60


mean observed adhesion forces and the number of snap-in events measured 

for each membrane are also tabulated in Table 5.6, based on the measurements 

taken from nine different points on each membrane surface. 

All measurements for P-P membrane contained snap-in events, but this 

decreased as the SPEEK content of the membrane increased. For the S5-20 

membrane, containing 5% SPEEK, no snap-in event was measured at all. 

As the SPEEK content of the membranes is increased, a substantive and 

systematic decrease in mean observed adhesion forces is seen, being a factor 

of almost 40 between P-P and S5-20 membranes. These trends together 

show the profound influence on the surface properties of the membranes 

of the incorporation of small amounts of SPEEK. It is also notable that the 

presence of snap-in events in some cases in the S-series membranes, except 

for S5-20, and the large standard deviation values show that some variability 

in the surface properties of the membranes exist. 

AFM has also been used to help in the assessment of fouling by 

humic acid (HA) of SPEEK-modified polysulphone membranes [30]. 

HAs are heterogeneous materials, containing three main types of functional 

groups: carboxylic acids, phenolic acids and methoxycarbonyls. 

They are mostly negatively charged for pH values above pH 2.8 [31]. 

Measurements were carried out with the S5-20 SPEEK membrane, and 

an aromatic PES membrane (ES404), which were chosen as a comparable 

commercially available membrane [30]. 

The effects of a deposited HA layer on membrane filtration will 

depend to some extent on its physical state. Images of membranes 

ES404 and S5-20 prior to use in filtering HA from water are shown in 

Figure 5.23(a). Before use, the S5-20 membrane has a rougher surface, 

visible in the images, and also indicated by a greater rms roughness. 

Figure 5.23(b) shows images of the two same membranes after 2 h filtering 

HA from model water. For the ES404 membrane the deposit is compact 

with occasional larger spheroidal aggregates. The rms surface roughness 

was greater by a factor of approximately 1.9 compared to before filtration. 

For the S5-20 SPEEK membrane, the deposit is much greater due to 

a higher flux [30]. The deposit is also less compact and more irregular than 

that seen for the ES404 membrane, and the rms surface roughness has 

increased by a factor of approximately 5.6 compared to before filtration. 

Both membranes were rinsed subsequent to filtration. Recovered membranes 

are shown in Figure 5.23(c). For the ES404 membrane, the surface 

roughness is similar to the fouled membrane, suggesting that rinsing has 

had little effect on removing the fouling aggregates. For the S5-20 membrane, 

however, the roughness value is greatly reduced from the fouled 

membrane, but has not quite returned to the value seen for the unused 

membrane. This suggests that most, but not all, of the fouling material 

has been removed by simple rinsing.

Å 

200 

100 

0 


ES404: R p-v 26.6 nm; R rms 1.6 nm S5-20: R p-v 33.7 nm; R rms 2.5 nm 

2 

2 

2 

1.5 

1.5 

1.5 

1.5 

µm 

1 

0.5 0.5 

1 

µm 

1 

µm 

0.5 

0.5 

1 

µm 

(a) 0 0 

0 0 

Å 

300 

200 

100 

0 

2 

1.5 

Å 

200 

100 

0 

ES404: Rp-v 39.9 nm; Rrms 3.0 nm S5-20: R 124.0 nm; R 14.1 nm 

p-v rms 

Å 

1000 

1 1 

0.5 0.5 

(b) 0 0 

Å 

300 

2 

200 

100 

0 

(c) 

1.5 

µm 

µm 

1 

ES404: R p-v 32.6 nm; R rms 2.9 nm 

0.5 0.5 

0 0 

1 

1.5 

2 

800 

400 

2 

0 

Å 

400 

300 

200 

100 

0 

2 

1.5 

µm µm 

1.5 

2 

1.5 

µm µm 

1 

0.5 0.5 

0 0 

2 

1.5 

1 

µm 

S5-20: R p-v 42.0 nm; R rms 3.9 nm 

1.5 

1 1 

µm 

0.5 0.5 

0 0 

fIgurE 5.23 AFM images of ES404 and S5-20 membranes: (a) fresh membrane, 

(b) membrane after 2 h of filtering HA in water, and (c) recovered membrane after rinsing. 

R p–v � peak to valley roughness; R rms � rms roughness. 

2 

2


The polymers from which the ES404 and S5-20 membranes are primarily 

constructed, PES and polysulphone, respectively, are similar in physical 

and chemical characteristics. However, the blending of SPEEK into the S5- 

20 has resulted in a greater surface charge, greater porosity and a greater 

roughness. These properties have also altered the way in which the HA 

deposits are structured. The much less compact nature of the HA layer on 

the S5-20 membrane has resulted in easier rinsing and cleaning, despite a 

higher deposition of material at the membrane surface. 

Membranes containing blended SPEEK, such as the S5-20 membrane, 

show a combination of permeability, rejection properties and low adhesion 

characteristics. Attraction and adhesion to the membranes by silica 

colloids have been shown to be much reduced. In addition fouling by HA 

has been shown to be easily removed by simple rinsing of the membrane 

surface due to the open and un-compact structure of the deposited layers. 

Further details of the development of PSU/SPEEK membranes are 

given in Chapter 4. 

5.5 ConCluSIonS 

In this chapter we have discussed the contribution that AFM may make 

in the development of biofouling-resistant filtration membranes. The ability 

to image the 3D topography of the membrane surface allows quantitative 

assessment of both roughness and PSD. Measurement of roughness before 

and after the use of a membrane gives a quantitative measure of the degree 

of fouling on the membrane and allows comparison between different 

membranes. The PSD gives an indication of porosity, which complements 

observations which may be made using other techniques. In addition the 

ability of the AFM to use the colloid probe technique to directly assess the 

interaction forces between colloids and membrane surfaces under different 

conditions is of great use when it comes to assessing the capability of 

newly developed membranes to reject fouling particulates. 

In the future AFM has the capabilities to make a significant contribution 

in the development of new membrane surfaces and their properties, both 

by allowing characterisation of surface morphology and by measuring the 

physical interactions between membranes and potential fouling materials. 

ACKnowlEdgEMEntS 

We thank all who have contributed to this research, especially Laila 

Al-Khatib and Victor Kochkodan for their contribution to this research.

AbbrEvIAtIonS And SyMbolS 

NOM Natural organic matter 

qDMAEMA Quaternary 2-dimethyl-aminoethylmethacrylate 

PES Polyethersulphone 

PVDF Polyvinylidene fluoride 

HEMA Hydroxyethyl methacrylate 

DM Degree of modification 

d p Measured pore size (diameter) m 

� Standard deviation of measurements 

� 0 Modal value of d p m 

PSD Pore size distribution 

BSA Bovine serum albumin 

SPEEK Sulphonated poly(ether-ether ketone) 

PEEK Poly(ether-ether ketone) 

HA Humic acid 

references 

ABBREvIATIONs AND syMBOLs 169 

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Langmuir 21 (2005) 7491–7500. 

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184 (1996) 594–600. 

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147–157. 

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surface modifications for the preparation of hydrophilic and low protein-adsorbing 

ultrafiltration membranes, J. Memb. Sci. 115 (1) (1996) 31–47. 

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(2005) 1025–1035. 

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1885–1903. 

[27] M. Nystrom, P. Jarvinen, Modification of polysulfone ultrafiltration membranes with 

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water production, Chem. Eng. Sci. 55 (2000) 5171–5175.

C H A P T E R 

6 

Nanoscale Analysis 

of Pharmaceuticals by 

Scanning Probe Microscopy 

Clive J. Roberts 

O U T L I N E 


6.2 The AFM as a Force Measurement Tool in Pharmaceuticals 174 

6.2.1 Particle Interaction Measurements 175 

6.2.2 Mechanical Properties from Single-particle Measurements 179 

6.3 AFM Imaging-Based Studies 183 

6.4 Micro- and Nanothermal Characterisation with SPM 185 





6.1 INTroduCTIoN 

There is an increasing demand to develop pharmaceuticals and biomedical 

devices with architectures and complex chemistries controlled at 

the nanoscale. The need to develop delivery systems capable of targeting 

specific sites in the body or to successfully formulate poorly soluble 

drugs frequently requires nanoscale solutions. For example, targeted systems 

typically employ nanoparticles, incorporating a number of elements 



174 6. NANOSCALE ANALySIS Of PHARMACEUTICALS by SCANNINg PRObE MICROSCOPy 

aimed at providing storage of the active therapeutic ‘stealth’ functionality 

to avoid the body defences as well as a targeting element. The additional 

trend towards the delivery of protein- and DNA-based medicines 

through new alternative delivery routes such as inhalation has also 

increased this need for nanoscale analysis. Such complex systems require 

analysis capable of minimal disruption due to sample preparation and 

the ability to operate in a ‘physiological’ environment. This demand 

often exceeds the capacity of traditional analytical approaches to provide 

an effective understanding of this new generation of therapeutics. 

This chapter will highlight the role of atomic force microscopy (AFM) 

and other scanning probe microscopies (SPM) in the qualitative and 

quantitative analysis of pharmaceuticals, highlighting both imaging and 

force data acquisition modes. These microscopes have enabled the study 

of pharmaceutical devices [1–3] and drug particles [4–6] with minimal 

pre-treatment in both air and liquid at the nanoscale level. The potential 

for SPMs, and AFM in particular, is now being exploited as an integral 

part of formulation, in both academic and industrial research. It is of 

course important to note that whilst SPM-based solutions do represent an 

increasingly important part of the analysis of pharmaceuticals, they are 

best applied with complementary approaches, such as Raman spectroscopy 

or diffraction-based techniques, which can provide chemically specific 

and 3D structural data. 

6.2 The AFM AS A ForCe MeASureMeNT Tool IN 

PhArMACeuTICAlS 

Most pharmaceuticals are produced as solid dosage forms (e.g. tablets, 

capsules, inhalable powders) and hence their manufacture inevitably 

involves the handling and manipulation of powdered materials. These 

powders can have particles ranging from submicron to many hundreds 

of microns in size. An understanding of how the mechanical properties 

of these particles and the forces between them influence factors such as 

processability and stability is an important feature of formulation development. 

Indeed, in some cases, the final form of the drug (and other 

materials in the medicine (the excipients)) is loose powder, as e.g. in a dry 

powder inhaler (DPI). Here then, the successful delivery of the drug itself 

relies on an intimate understanding of particle properties and their interactions. 

Until recently, the direct assessment of particle-particle and particle-device 

interactions relied upon long-established bulk methods that 

deal with large numbers of particles, such as the centrifugal technique 

[7, 8]. Whilst effects such as cohesion and adhesion phenomena can be 

studied, these data reveal little concerning the nature and interplay of the

6.2 THE AfM AS A fORCE MEASUREMENT TOOL IN PHARMACEUTICALS 175 

fundamental forces involved (e.g. van der Waals, electrostatic, capillary). 

Access to such information is beneficial not only to the assessment of a 

formulation, but also to establish the basis of any required particle modification 

and optimisation. 

Just as particle interactions can be probed using AFM, the nanoscale 

mechanical properties of powders can also be investigated. Previously, 

this could only be derived from bulk techniques, where powders are 

compressed into miniature beams and three-point bending tests are 

performed. The need for relatively large amounts of powder and to 

account for the porosity of the beams has limited the applicability of this 

approach. Even using miniaturised beams, milligram quantities of material 

are required, preventing screening of active pharmaceutical ingredients 

at early stages of development [9, 10]. Here, we consider how AFM 

has been used to address both particle interactions and the measurement 

of the mechanical properties from single particles. 

6.2.1 Particle Interaction Measurements 

The ability to study single-particle interactions and the forces involved 

became possible with the advent of the AFM in 1986 [11–13]. In particular, 

the use of AFM in the so-called ‘colloidal probe’ technique, whereby 

the force of interaction between a spherical bead attached to the AFM 

cantilever and a planar surface was studied, revealed the potential of this 

approach [14]. Importantly, a single particle (e.g. drug) attached to the 

AFM cantilever can be used for a series of comparative experiments challenging 

different substrates. In addition, the ability of AFM to work in a 

variety of environments, such as controlled humidity and in liquids, is 

significant for pharmaceutical applications. 

The first example of this approach being used for a pharmaceutical 

powder examined the differences in the adhesion of lactose particles to 

two gelatin DPI capsule surfaces [15]. It is important when attaching 

such individual drug particles to an AFM cantilever that their contacting 

region remains free from any adhesives employed or damage during 

attachment. An example scanning electron microscope (SEM) image is 

shown in Figure 6.1, where a drug particle is attached to an AFM cantilever. 

Typically, to prepare such a probe would involve the use of a minute 

amount of glue on the end of the cantilever to which a particle is attached 

using a micromanipulator or the AFM itself. This relatively labourintensive 

sample preparation currently limits the number of different 

particles used within one study (usually to no more than five). The accessible 

particle size is typically in the range between 0.5 �m and 50 �m. For 

very small and/or cohesive particles (1 �m or less), more than one may 

become attached to the lever; however, as long as only one comes into 

contact with the surface to be challenged, this is acceptable.


500 nm 

AFM cantilever 

Drug particle 

FIgure 6.1 SEM image of the end of an AFM cantilever to which a single drug particle 

has been attached. The lower extremity of this particle forms the contact region with a sample 

surface being studied within the AFM. 

Having manufactured a particle probe, the forces of interaction of this 

probe with a surface are recorded. Figure 6.2 illustrates a schematic of a 

force curve and the main stages in acquiring such single-particle adhesion 

data. If such data is to be quantified in terms of force, then the 

spring constant of the AFM lever needs to be determined to enable calibration 

[16]. To ease comparisons between different-particle adhesion 

measurements, it is important to control key environmental factors such 

as humidity and to keep such instrument parameters as maximum presson 

force, contact time, particle approach and retract speed constant. 

Many researchers have now exploited this approach to explore particle 

interactions between drug and excipient particles and the components 

of delivery devices. Louey et al. used this approach to measure pulloff 

forces between a model colloidal silica probe and lactose particles 

suitable for use as carriers in a DPI [17]. AFM has also been used to 

rank the force of interaction of salbutamol with materials relevant to its 

inhaled delivery in the following manner, glass � lactose � salbutamol � 

polytetrafluoroethylene (PTFE), showing that on PTFE tribocharging 

occurred following repeated contact [18]. Using AFM in this way has 

also revealed the effect of inducing amorphous content on the surface of 

particles of the drug zanamivir, where an increase in its affinity with a lactose 

carrier surface was observed [19]. Such surface amorphous material is 

important from a pharmaceutical perspective as this will be more soluble 

and probably less stable than a crystalline form of the drug, and hence can 

cause desirable (or undesirable) effects in terms of increased amounts of 

drug delivered on administration and stability problems in a medicine.


(a) 

Cantilever deflection (nm) 

(b) 

Motion of 

lever 

0 

AFM cantilever 

with drug particle 

Sample 

Particle approaching sample 

Particle adhered 

to sample 

Particle detached 

to sample 

0 

Relative veticle position of sample and particle (nm) 

FIgure 6.2 (a) Schematic illustrating an AFM probe with attached drug particle coming 

to, contacting with and being removed from a sample surface. (b) With data recorded 

from such an event, the cantilever deflection can be converted to a force of the spring constant 

if the lever is known and the relative positions to a true sample-particle separation if 

the sensitivity of the microscope has been calibrated. 

The influence of relative humidity on the forces between particles is 

an important consideration in pharmaceuticals as this can strongly influence 

the stability of a medicine through the mediation of solution-based 

processes owing to surface adsorbed water. In addition, owing to the formation 

of capillary bridges between particles with increased humidity, 

this may cause aggregation. Hence, the effect of humidity has been the 

subject of a number of AFM studies. Young and co-workers have shown 

that drug cohesion increases at elevated humidity for some materials but 

decreased for others, potentially as a result of long-range attractive electrostatic 

interactions [20]. A variation in particle-contact morphology has 

also been shown to cause similar behaviour with increasing humidity 

[21]. The ability to record force data in controlled environments has been 

extended to work in liquids, e.g. to rank interactions in model propellants 

so as to simulate the environment within a pressurised metered dose 

inhaler [22–24].


These and other studies can broadly be divided into two types: those 

that rank relative particulate interactions and those that attempt to make 

a quantitative comparison of force per unit area of contact. Ranking studies 

address, e.g., how drug-drug cohesion compares to drug-excipient 

particle and drug-device adhesion. Since particulate interactions are dominated 

by aspects such as surface morphology, surface roughness, exposed 

chemical moieties and thermodynamic properties, all of which can vary 

from particle to particle and indeed within a single particle, such ranking 

comparisons are normally made using the same particle to challenge 

all the possible combinations of interactions. In this case, ranking should 

be consistent for each drug particle probe, but the absolute values of adhesion 

force determined cannot be used to make comparisons from particle 

to particle or between materials [18]. 

To quantify such measurements, particle variability and a lack of direct 

knowledge of the contacting regions must be overcome to allow the 

determination of factors such as surface energy and work of adhesion. 

The use of AFM to determine such properties on model flat surfaces, such 

as silicon, was established relatively early [25]. However, its application 

to pharmaceuticals due to difficulties of rough and variable particle morphology 

came later [19, 21, 22]. In these works, the principal variable that 

is allowed for is contact area. Contact areas have, to date, been estimated 

either via a direct imaging approach [22] or indirectly through imaging 

indents made by the particle probe in a plastic polymer film [19]. The 

subsequent use of adhesion models such as Johnson–Kendall–Roberts 

and Derjaguin–Muller–Toporov can then allow the surface energy of the 

particle (over the region of contact) to be determined. In this way, e.g., 

micronised (milled) salbutamol sulphate and a version prepared via a 

novel supercritical fluid method have been compared [22]. 

An alternative to this approach of trying to model the variable contact 

region between particles is to compare ratios of cohesive and adhesive 

forces between different particles rather than actual separation forces. 

This has allowed an assessment for relatively flat crystals of the affinity 

of salbutamol sulphate to lactose and budesonide to lactose, showing 

that salbutamol sulphate has a stronger affinity for lactose [26]. This 

information was then related successfully to the likely blend uniformity 

these materials would form. 

In addition to monitoring force normal to a surface, AFM is also capable 

of assessing frictional forces between a probe and a surface. This is 

achieved by recording the twist of the cantilever in addition to its vertical 

bend as it scans a surface in continuous contact with that surface 

(Figure 6.3a). This approach has recently been used to obtain singleparticle 

friction measurements on DPI formulations [27] and blister 

packaging material (used in DPIs) [28] and provides an opportunity to 

consider sliding as well as separation forces. Figure 6.3 shows examples


(a) (b) 

Scan 

direction 

(c) 

Position 1 

Lateral 

force 

signal 

Position 2 

Particle A 

Particle B 

Particle C 

PTFE Glass Zanamivir Zanamivir Magnesium 

� 

Magnesium 

stearate 

stearate 

PTFE 

of the results of recording the sliding friction of single lactose particles 

on various drugs, excipients and materials used in inhaler devices. This 

showed a ranking of glass�zanamivir � zanamivir–magnesium stearate 

blend�magnesium stearate�PTFE (see Figure 6.3c). The addition of magnesium 

stearate (a commonly employed lubricant) to the drug zanamivir 

was seen to dominate the behaviour of this system and significantly 

reduced the friction [27]. 

6.2.2 Mechanical Properties from Single-particle Measurements 

Consideration of the schematic force distance curve in Figure 6.2(b) 

reveals that not only can adhesion data be determined, but if the region 

of contact is considered where the probe is pressed into a surface and 

is then withdrawn, then it is clear that this contains information on 

the mechanical properties of the sample. Indeed, data gathered from a 

nanoscale contact in this manner is similar to traditional indentation 

Drug 

MgSt 

Glass 

Drug � 

MagSt 

FIgure 6.3 (a) Schematic of AFM particle friction set-up. Position 1: low-friction surface 

causes very small lateral force on cantilever. Position 2: high-friction surface causes 

large lateral force and cantilever twists. Inset: SEM image of lactose particle attached to cantilever. 

(b) 5 �m � 5 �m topographic AFM images of surfaces under study. From the top, 

clockwise: PTFE; glass; the drug zanamivir with magnesium stearate; magnesium stearate 

and zanamivir. (c) Processed data showing friction on all surfaces for three lactose particles.


measurements more typically measured on a micron or greater scale to 

determine elastic modulus and hardness [29]. There are, however, a number 

of limitations of the AFM data that must first be considered. First, 

as standard AFM cantilevers are typically very flexible (so that they are 

sensitive to nanoNewton forces), they are incapable of deforming surfaces 

beyond approximately 10 GPa elastic modulus. Second, unlike a 

traditional indenter, an AFM probe does not approach or deform a surface 

completely normal to that surface, because of the need to have the 

lever at a slight angle to ensure that the probe apex contacts the sample 

first. This causes lateral deformation errors in the data, which are only 

negligible with relatively small indent depths. 

Despite these issues, many groups have employed AFM to determine the 

elastic, inelastic and hardness properties of materials. Such deformation 

behaviour of pharmaceutical ingredients is known to affect pharmaceutical 

processes such as milling and compaction [30–33]. To date, most 

reported pharmaceutical examples of this approach have used a modified 

AFM equipped with a relatively large probe with well-defined 

geometry and a much stiffened spring that supports this probe [30, 

34, 35]. Typically, in these methods, material parameters are extracted 

from load-displacement unloading curves using approaches outlined by 

Oliver and Pharr [36]. Recently, Ward and co-workers [37] have utilised 

a sharp AFM probe and normal cantilevers to record nanomechanical 

measurements on sorbital samples to quantitatively distinguish between 

amorphous and crystalline domains through Young’s modulus measurements. 

Figure 6.4 shows images and typical force distance curves 

obtained from crystalline and amorphous sorbitol regions and a control 

of a hard, non-indenting silicon substrate. To determine the nanoindentation 

of the probe tip into the sorbitol sample as a function of load, 

the force distance curves from the sorbitol sample and the control hard 

substrate were compared. When comparing the amorphous and the 

crystalline regions, it is the amorphous region that provided the greater 

deflection of the tip (indicating the softer material and greater indentation) 

at the given applied loads [37]. In this approach, a comparison of 

the gradients of the contact region of the force distance curves between 

a hard non-deformable reference surface and the sample can provide the 

relative stiffness of a surface [38]. By applying the Hertz model [39] to 

the nanoindentation data, a quantitative value of the Young’s modulus of 

the surfaces can be obtained. The Hertz model describes the elastic deformation 

of two homogenous surfaces under an applied load and is often 

used to model AFM data since it requires little knowledge of parameters 

such as surface energy. The first step in modelling the data is to compare 

force distance curves recorded on the sample and an ideally hard reference 

(glass surface) to determine the indentation (�) of the probe into the 

sample as a function of load. The contact regions of the curves are overlaid 

such that zero force is equal to zero indentation.

(a) 

4 µm 

0 

(b) 

4 µm 

0 


Force (nN) 

(e) 

8 

7 

6 

5 

4 

3 

2 

1 

0 

�1 

Retracting 

0 20 40 60 

Log E (Pa) 

Force (nN) 

The value of indentation can then be related to the combined elastic 

modulus of the tip and the sample (K) by: 

L 

K � 

( � R) 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

3 2 

0 50 100 150 

Relative z (nm) 

200 250 300 

1 

1. Si Reference 

2. Crystalline 

3. Amorphous 

1.0 � 10 8 

1.0 � 10 7 

1.0 � 10 6 

1.0 � 10 5 

1.0 � 10 4 

2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 

Load (nN) 

Extending 

80 100 120 140 160 180 

Relative z (nm) 

3 1/ 2 

8 

Crystalline 

Amorphous 

FIgure 6.4 (a) AFM images of unmodified sorbitol (topographic height and phase 

images), insert highlights banding pattern; (b) AFM images within a quench-cooled 

domain of sorbitol, which would be expected to have a more amorphous nature; 

(c) nanoindentation curves for the crystalline and amorphous domains; (d) load dependence 

on Young’s modulus and (e) force curve from the amorphous domain. Reproduced 

with permission [37]. 

(6.1) 

where L is the load and R is the radius of the probe. Since the combined 

elastic modulus contains the elastic moduli for the tip and the sample, 

(c) 

(d)


an expression containing the E s, the elastic moduli of the sample can be 

obtained: 

� t � s 

K � � 

E E 

� 

4⎛ 

2 2 

1 υ 1 υ ⎞ 

⎜ 

3 ⎝⎜ 

⎠⎟ 

t 

s 

1 

(6.2) 

where ν t and ν s are the Poisson’s ratio of the tip and the sample, respectively. 

Since E t is much greater than E s, the first term in the bracket of 

equation (6.2) may be ignored to produce equation (6.3): 

E 

s 

3K( 1 � υs) 

� 

4 

Combining equations (6.1) and (6.3) derives: 

E 

s 

2 

2 

3L( 1 � υs 

) 

� 3 1/ 2 

4( 8� 

R) 

(6.3) 

(6.4) 

The value of ν s is difficult to determine accurately for many samples 

such as sorbitol and other pharmaceutical materials. Therefore, it is 

appropriate to use a midrange value of ν s (typical range is from 0.1–0.5) 

since varying this has little effect on the value obtained for E s. 

The Hertz model is valid only for elastic deformation, so it is important 

to remove any contribution from inelastic deformation from the analysis. 

The model also assumes no significant adhesion between the probe and 

sample. To overcome this, only data from the loading curve is typically 

used. To assess the validity of the data for use with the Hertz model, a plot 

of load versus indentation is typically produced. In the ideal situation, a linear 

relationship between load and indentation should be observed to allow 

E s to be calculated. The Young’s modulus values for the amorphous regions 

of the sorbitol using this type of analysis of Ward et al. were less than the 

crystalline regions [37]. Interestingly, the Young’s modulus values appeared 

to rise with increases in loading in both amorphous and crystalline regions 

of sorbital, suggesting possible viscoelastic/plastic deformation [37]. Hence, 

these surface mechanical measurements were able to distinguish between 

crystalline and amorphous material and exemplify the possible use of the 

AFM to screen batch-to-batch variations in drug formulations. 

In general, it can be seen, therefore, that AFM provides a very flexible 

platform, adaptable to a range of experimental geometries for force measurements 

with real pharmaceutical materials. Examples of determining 

the interaction between an iron-coated AFM probe and a range of drugs 

to simulate tablet press–tablet interactions [40], and particle-bubble interaction 

forces in the mineral processing industry [41] give an idea of other 

possibilities yet to be fully explored.

6.3 AfM IMAgINg-bASEd STUdIES 183 

6.3 AFM IMAgINg-BASed STudIeS 

As a microscopy, AFM is perhaps better known for its ability to image 

surfaces at nanometre resolution in a variety of environments than as a 

force measurement tool. As a material under study can be exposed to 

environmental stresses (temperature, humidity, solvents etc.), it can often 

be in a dynamic state and hence, as long as the kinetics are not too rapid, 

AFM is able to provide a dynamic view of surface-mediated processes 

(unless employing advanced video rate imaging AFM [42], a typical 

1 �m � 1 �m image takes approximately 30 s to acquire). This approach 

has found effective applications in pharmaceuticals in the study of environmental 

stress on the surface properties of formulations, drug release 

from erodible materials and crystallisation phenomena. 

Price and Young [43] have studied the real-time effects of changes in 

relative humidity (RH) on spray-dried lactose using environmentally 

controlled AFM. The lactose was imaged at 0%, 30% and 58% RH for 4, 2 

and 22 h, respectively. Recrystallisation of amorphous lactose, promoted 

by the presence of water, was observed at 58% and 75% RH, although 

only some of the particles were shown to undergo nucleation and crystal 

growth. The AFM data was combined with traditional approaches 

such as X-ray powder diffraction, differential scanning calorimetry and 

dynamic vapour sorption and was shown to have significant potential 

for studies of the nucleation and crystallisation processes of amorphous 

material [43]. 

Li and co-workers have utilised contact mode AFM imaging in air to 

image a series of partial dissolutions on the (010) face of paracetamol 

[44]. From the AFM images of the (010) face of acetaminophen crystals 

treated with alternative dissolution solvents, different etching patterns 

were observed. These different etching patterns were speculated to be a 

result from the surface diffusion of the crystal molecules desorbed during 

the dissolution process and by the mutual interaction between the 

solvent and crystal molecules. AFM has similarly been employed to 

visualise the effect of dissolution media on various polymeric systems 

designed to achieve a specific drug-release profile [45]. 

It is widely known that pharmaceutical additives and impurities in 

drug formulations can affect drug crystal growth, morphology and potential 

drug efficacy. This may be achieved deliberately to control crystal 

habit or an undesirable consequence of contamination. By understanding 

the degree to which impurities affect these critical formulation parameters, 

drug delivery systems can be developed more effectively. AFM has 

the capability to study drug crystal changes in real time, as demonstrated 

by Thompson et al. in the study of paracetamol in the presence of impurities, 

acetanilide and metacetamol using AFM in liquid [46]. A series of 

real-time AFM images of the (001) face of a native paracetamol crystal are


FIgure 6.5 A sequence of 10 �m � 10 �m AFM images of the (001) face of a paracetamol 

crystal during incubation in paracetamol solution. In image (a) time t � 0 s, (b) t � 60 s, 

(c) t � 118 s, (d) t � 176 s, (e) t � 234 s and (f) t � 292 s. Figure reproduced with permission [46]. 

shown in Figure 6.5, and illustrates that the growth steps of crystallisation 

over 4.8 h are curved in appearance, indicative of crystal growth via 

the screw dislocation mechanism. AFM images of the (001) face of another 

paracetamol crystal during incubation with 4 mol% acetanilide over time 

are shown in Figure 6.6. The defects in the crystal surface form weak 

points, leading to deepened holes (one hole is highlighted by a black 

arrow in Figure 6.6) over 12 h, indicating that the dissolution occurs both 

laterally and towards the crystal core [46]. Images during incubation with 

4 mol% metacetamol showed that the steps formed were significantly 

smaller and pointed in appearance (image not shown here). These features 

were ascribed to ‘pinning’, an effect caused when additives adsorb 

onto the steps and force them to grow between the impurities [46]. 

From our consideration of AFM as a force measurement tool, it is clear 

that the probe is sensitive not only to topography but also to the magnitude 

and nature of the forces experienced by the probe. Consequently, 

whilst imaging, if such sensitivity can be mapped also, it becomes possible 

to produce alongside topography data sensitive to a particular surface 

property (e.g. adhesion, harness etc.). For example, during the commonly 

employed tapping mode imaging [47], where the AFM cantilever is oscillated 

at its resonant frequency and intermittently contacts a sample surface 

at the bottom of each oscillation cycle, the phase of the oscillation as well as

6.4 MICRO- ANd NANOTHERMAL CHARACTERISATION wITH SPM 185 

FIgure 6.6 A sequence of 10 �m � 10 �m AFM images of the (001) face of a paracetamol 

crystal in paracetamol/4 mol% acetanilide solution. The dissolution of step one 

is followed by a black arrow on each image. Image (a) is taken 11.5 min after addition of 

paracetamol/4 mol% acetanilide solution. Images (b–f) are taken at the following times 

after image (a): (b) t � 146 s, (c) t � 290 s, (d) t � 436 s, (e) t � 582 s and (f) t � 728 s. Figure 

reproduced with permission [46]. 

the topography can be recorded. Phase images are obtained by measuring 

the phase lag between the signal that drives the cantilever-tip oscillation 

and the output signal of the cantilever oscillation (will differ more to the 

original cantilever-tip oscillation if the sample surface is soft and viscoelastic 

due to greater energy lost to the sample). The use of phase imaging 

alongside topographical imaging is particularly useful for studying drug 

polymorphs phase-separated systems and drug-excipients systems as it 

can be used to map out a profile of materials with different mechanical and 

physicochemical properties [48, 49]. 

6.4 MICro- ANd NANoTherMAl 

ChArACTerISATIoN wITh SPM 

Knowledge of the distribution and physical form of a drug in its 

formulation is important in determining its overall performance and 

can further our understanding into bioavailability issues in medicines. 

Classically, one of the main tools used to identify the form a drug takes 

within a formulation and the interactions between its components is


calorimetry. However, such approaches cannot reveal the spatial distribution 

of these components. An adaptation of AFM that can achieve this is 

the Scanning Thermal Microscope (SThM) [50]. Here, the normal silicon 

cantilever is replaced with a Wollaston wire probe, brought to a sharp 

apex in the form of a cantilever. The spatial (and thermal mapping) resolution 

of such probes is on the order of a micron. Whilst this is useful, 

they also have the additional ability to apply heat locally to a surface and 

to record the power required to deliver a constant temperature increase to 

that point in the sample (in a manner analogous to Differential Scanning 

Calorimetry (DSC)), therefore providing detailed thermal characterisation 

at that point on a sample (the so-called Local Thermal Analysis (LTA)). 

To date, LTA has been the main area of application of this approach in 

pharmaceuticals. 

Six et al. have demonstrated the ability of SThM analysis to distinguish 

and identify phase-separated material in solid dispersions of 

itraconazole and Eudragit ® E100 polymer [51]. Such dispersions of 

a poorly soluble drug in a soluble matrix represent a classic route to 

improving the bioavailability of such drugs. SThM images of dispersions 

containing 10%, 40% and 60% itraconazole showed an increase in 

surface roughness with an increase in drug loading, possibly linking the 

rough surface areas to phase-separated drug. Phase-separated regions of 

the drug are not desired as they would be less liable to release the active 

ingredient than molecular dispersed drug. LTA has been used to characterise 

the different phases by a comparison of the glass transition (T g) of 

different dispersions with that of the pure compounds of drug and polymer. 

LTA showed that the penetration of the probe tip into a sample of 

pure itraconazole occurred at around 333 K, which is in good agreement 

with the previously determined T g for the drug by DSC of 332.4 K. In contrast, 

the penetration of the probe tip into pure Eudragit ® E100 occurred 

at a much higher temperature of 383 K compared to its T g of 318 K determined 

by DSC and was linked to the fragility of the sample [51]. It was 

also observed in dispersions with low drug loading (10%) that the probetip 

penetration was at a temperature in between the T gs for itraconazole 

and Eudragit ® E100, an indication of intimate mixing of the components. 

At high drug loading (60%) dispersions, the T g was similar to that for the 

drug, indicating separation of the components. 

In another study by Sanders et al. [52], SThM combined with LTA 

was used to distinguish between two polymorphs of cimetidine, types 

A and B. These two pharmaceutically useful anhydrous polymorphs of 

cimetidine had previously been tentatively distinguished by AFM phase 

imaging in a variable humidity environment [48]. An understanding 

and ability to detect and distinguish between different polymorphs in 

drug formulations is of particular significance, as different polymorphs 

can have different physicochemical properties and can convert from one


form to another under storage conditions. While cimetidine is known to 

have seven polymorphs, only type A and type B are used in tablet and 

suspension formulations, respectively [53]. SThM images were obtained 

using a probe temperature of 50°C and a scan rate of 1 Hz. Figure 6.7 

shows topographical (images a and c) and SThM images (images b and d) 

of a 50:50 mixture of polymorph type A and type B from two different 

areas. The contrast highlighted by arrows in images b and d is a result of 

the differences in surface thermal conductivity in the two different polymorphs. 

LTA on discs of pure samples of polymorphs type A and type B 

were used to help elucidate that the lighter and darker regions observed 

in the topographical data (Figure 6.7a, c) were of polymorphs type A and 

FIgure 6.7 50 �m � 50 �m images of a pressed disc comprising a 50:50 mixture of the A 

and B polymorphs of cimetidine (scale bar: 10 mm): (a) and (c) show topographical images of 

two different areas of the disc and (b) and (d) show the corresponding thermal conductivity 

images. Features highlighted with arrows show contrast as a result of the differing thermal 

behaviour of the two polymorphic forms of cimetidine. Reproduced with permission [52].


type B, respectively. LTA was performed with a temperature ramp rate 

of 10°C s �1 . Figure 6.8 shows the local thermal analysis of polymorphs B 

and A with melting points observed between 140–146°C and 141–143°C, 

respectively. The close range of melting points for polymorphs A and B 

illustrates why bulk thermal analytical methods have difficulty distinguishing 

between the two polymorphs. An interesting feature of the data 

for polymorph A is the endothermic peak seen just above 100°C (marked 

X in Figure 6.8b). This feature is seen in neither the bulk thermal analysis 

of form A nor LTA of form B. This would suggest that this feature is a 

result of the increased surface sensitivity of the localized measurements, 

and that this endothermic peak is likely to be a result of adsorbed surface 

water. This is consistent with form A being more hydrophillic than form 

(a) 

Sensor movement (μm) Sensor movement (μm) 

(b) 

1.5 

0 

–1.5 

–3 

1 

0 

–1 

–2 

(I) 

(III) 

20 60 100 140 

Temperature (°C) 

(I) 

(III) 

20 

60 

100 180 


FIgure 6.8 Localised thermal analysis of pure cimetidine polymorphs (a) B and (b) A. 

Lines denoted (I) show the calorimetric data for a single point and dashed lines (II) show 

the movement of the sensor during the measurement, corresponding to thermomechanical 

analysis. Lines (III) and (IV) show similar data for other points on the samples. Reproduced 

with permission [52]. 

(II) 

(IV) 

(IV) 

(II) 

1 

0 

1 

0 

–2 

–4 

–2 

–2 

Derivative power (μW deg –1 ) 

Derivative power (μW deg –1 )


B and with previous AFM data, which displayed a behaviour indicative 

of adsorbed water at the surface [48]. 

These and other results not only demonstrate the ability of LTA to thermally 

characterise individual components within formulation mixes, but 

also highlight the limitation of the system to detect structures of approximately 

20 �m � 20 �m or larger, such that if more than one structure 

is present in a region, the LTA measurement appears as an intermediate 

softening of values between individual components. 

Clearly, replacement of the traditional AFM imaging probe with a 

heat-conductive Wollaston wire has enabled the local thermal properties 

of pharmaceuticals to be investigated but at the sacrifice of spatial resolution. 

However, the recent development of a commercially fabricated 

doped-silicon cantilever with a heated probe has enabled this problem 

to be overcome and for nanoscale thermal events with nanometre precision 

to be probed [54]. This nanothermal cantilever has a conductive coating 

through which an electrical current is passed to an integrated heater 

located directly above the probe. By varying the resistance of the circuit, 

the temperature of the heater can be controlled up to 500°C, depending 

on the choice of probe. When the probe is in contact with the surface, any 

deflections in the cantilever are recorded and this can reveal the nature 

of the material (e.g. amorphous versus crystalline) [55, 56] and the occurrence 

of thermal phase transitions such as melting or glass transitions [54]. 

The development of the nanoprobe has also given the ability to maintain 

a constant probe temperature during scanning to allow for thermal imaging 

of the surface or for controlled thermal nanolithography [57, 58]. An 

example of such local thermal analysis is shown in Figure 6.9, where an 

Deflection (arb. units) 

Dehydration 

Melt 

50 100 150 200 


FIgure 6.9 Nanoscale thermal analysis (NTA) of lactose monohydrate. (Left) Image 

recorded with an NTA probe after local thermal analysis has been performed at the area, highlighted 

with an arrow. The nanoscale pit is the result of local melting. (Right) Corresponding 

cantilever deflection trace, revealing dehydration and melting of the lactose monohydrate.


individual lactose monohydrate crystal within a blend has been studied. 

The resultant indent due to local melting is apparent in the image (now 

with nanometre resolution due to the sharper probe). The corresponding 

cantilever deflection trace reveals the loss of water from the monohydrate 

and the melt of the anhydrous form at temperatures consistent with previous 

SThM and bulk analysis [59]. 

6.5 CoNCluSIoNS 

As the barriers to developing new medicines become ever greater 

owing to new challenges in delivery, greater regulation and the scarcity 

of ‘easy’ molecules to develop into medicines, the role of probe microscopes 

in pharmaceuticals development is set to increase. The advantages 

of nanoscale resolution, minimal sample preparation and the non-invasive 

imaging capabilities of AFM in particular make this an ideal tool to bring 

new approaches to the investigation of drug material properties. 

This chapter has provided an insight into the improved understanding 

of pharmaceutical drug development available by AFM and thermal 

versions of AFM. These approaches have in a relatively short period of 

time provided a series of new insights into drug particle interactions 

and formulation structure. The capacity of AFM to not only image at the 

nanoscale but also to investigate interactions and to spatially map surface 

properties and to operate in a variety of environments consistent 

with pharmaceutical testing, manufacture and delivery provides great 

opportunity. 

ACkNowledgeMeNTS 

I would like to thank all who have contributed to this research, especially 

Martyn Davies, Jennifer Hooton, Ardeshir Danesh, Jin Zheng, Jeff 

James, Matthew Bunker, Michael Davies and Anne Turner. 

ABBrevIATIoNS ANd SyMBolS 

DPI dry powder inhaler 

Es elastic modulus of sample N m�2 K combined elastic modulus of tip and sample N m�2 L load force N

LTA local thermal analysis 

PTFE polytetrafluoroethylene 

R radius of probe m 

SThM scanning thermal microscopy 

T g glass transition temperature °C 

v s 

v t 

Poisson’s ratio for sample 

Poisson’s ratio of tip 

� indentation depth m 

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C H A P T E R 

7 

Micro/Nanoengineering and 

AFM for Cellular Sensing 

Huabing Yin, Gordon McPhee and 

Phil S. Dobson 

O U T L I N E 


7.1.1 How Do Cells Respond to the ECM? 196 

7.2 Engineering the ECM for Probing Cell Sensing 198 

7.2.1 Surface Patterning (Chemical Signals) 199 

7.2.2 Nanotopography 205 

7.2.3 Nanoscale Measurement: Challenges and Opportunities for AFM 209 

7.3 AFM in Cell Measurement 211 

7.3.1 AFM Imaging of Cells 211 

7.3.2 Elasticity Measurement of Living Cells 214 





7.1 IntroduCtIon 

Cells live in a complex extracellular matrix (ECM), which consists of 

neighbouring cells, proteins and extracellular fluids, inside the bodies of 

animals and plants. Cells constantly monitor the chemical and physical 

signals from their surroundings and react accordingly. A large body of 



196 7. MICRO/NANOENgINEERINg ANd AFM FOR CELLULAR SENSINg 

evidence has shown that the various interactions between a cell and different 

microenvironments play crucial roles in embryonic morphogenesis, 

tissue formation and maintenance of physiological functions [1]. Perturbations 

of cellular microenvironments or the adhesion of cells to the ECM 

can cause genetic defects, autoimmune diseases and cancers [2, 3]. It is 

also well known that in cancer metastasis, malignant cancer cells are able 

to break down tissue architecture and invade distant organ sites [4, 5]. 

The ECM is an intricate network within which biomolecules are 

precisely organised [6]. Classes of structural ECM proteins, mainly, collagen, 

glycoproteins and proteoglycans, form highly organised nanoscale 

structures, providing cells with both biological information and physical 

scaffolds for adhesion and migration. Although the regulatory functions 

of soluble factors (i.e. growth factors and hormones) present in the ECM 

have been well investigated, it has recently become increasingly recognised 

that the physics and mechanics of the ECM also have a significant 

impact on cell function and fate. Revealing the precise mechanisms underlying 

these processes is intrinsically challenging – the events happen at 

many dimensions from single molecules to the macrotissue level, and in a 

dynamic/collective and hierarchical manner. 

In order to better understand the interactions between the cells and 

the ECM and subsequent responses, engineered substrates and scaffolds 

are being developed to replace the native ECM. This has required inputs 

from many fields, ranging from surface engineering, material science and 

tissue engineering to cell biology. In this chapter, we will describe current 

developments of micro- and nanoengineered ECM materials and 

structures for the investigation of adhesion-associated responses of cells 

to chemical and mechanical cues. These efforts will be illustrated by an 

interconnected set of examples. 

Importantly, as the length scales being examined in these studies have 

progressively shrunk, progress in interpreting the nanoworld has become 

increasingly dependent on techniques capable of nanoscale measurements 

within physiologically relevant environments. In this context, atomic 

force microscopy (AFM) has emerged as a powerful and multifunctional 

nanoscale tool, opening exciting new possibilities to address mechanistic 

questions in cell biology that may facilitate the development of efficient 

therapies for human health. In the following sections, we briefly introduce 

the basic biological principles for adhesion-associated cell sensing, 

followed by the engineering methods involved in generating substrates 

and materials to study cellular interactions, and finally the methodology 

associated with AFM measurements on these systems. 

7.1.1 How do Cells respond to the ECM? 

First, we review two important subcellular systems that are of fundamental 

importance in cell adhesion to the ECM: the cell membrane and

7.1 INTROdUCTION 197 

the cytoskeleton (Figure 7.1) (for background reading see, Alberts et al. [7]). 

The cell membrane is a barrier that separates the interior of the cell from 

the outside environment; it regulates the transport of molecules into and 

out of the cell and maintains the interior of the cell at optimal levels of pH 

and ionic concentrations. Cell membranes are primarily made of a selectively 

permeable lipid bilayer, containing various functional proteins that 

are involved in a range of specific cellular activities. For example, 25–50% 

of membrane receptors may be adhesive receptors [8]. The interior compartment 

next to the cell membrane is the cytoplasm. This accommodates 

a number of specialised subcellular organelles that cooperate to maintain 

cell function. The cytoskeleton, which is located within the cytoplasm, is 

made up of three types of long rod-shaped molecules: microfilaments (e.g. 

actin stress fibre), microtubules (e.g. tubulin) and intermediate filaments 

(e.g. vimentin). These molecules attach to one another, link to other subcellular 

systems, such as the cell membrane and cell nucleus, and build 

a framework to give the cell both shape and movement. The configuration 

of the cytoskeleton dynamically adapts during cellular processes and 

undergoes microscopically observable morphological changes. 

It is now clear that a particular family of transmembrane cell surface 

receptors, the integrins, mediate many of the interactions between a cell 

and the ECM. They both recognise peptide sequences, such as Arg-Gly-Asp 

(RGD) within the chains of certain ECM proteins (e.g. fibronectin), and 

connect the cytoskeleton to the ECM. During this process, adhesive 

contacts between the cell and the ECM are formed [9]. A common type 

of adhesive contact involves multiprotein complexes, called focal adhesions. 

These comprise integrins, the associated cytoplasmic proteins, 

and a number of protein kinases [1, 10]. Focal adhesions are the major 

sites for actin stress fibre attachment and thus a connection between the 

cytoskeleton and the ECM. Integrins that are bound to the ECM transmit 

Nucleus 

Focal adhesion 

Cell membrane 

F-actin stress fibre 

Direction of motion 

ECM or substrate 

Microtubule 

Filopodium 

Pseudopodium 

Lamellopodium 

FIgurE 7.1 Schematic drawing of cell adhesion to an ECM or substrate. The cell 

adheres firmly to the ECM through focal adhesions (a multiprotein complex). The focal 

adhesions are the sites for the attachment of F-actin stress fibres – one type of cytoskeleton 

protein. Filopodium and lamellopodium are located at the leading edge for cell to migrate.


mechanical stress across the plasma membrane and convey the traction 

force that develops in the cytoskeleton to the ECM. Unbound integrins 

are mobile within the cell membrane and readily form clusters and focal 

adhesions in a tension-dependent manner [11]. Integrins also participate 

in other signalling transductions that regulate cell growth [12]. 

During the initial phase of cell adhesion, interactions between the 

integrins and the ECM ligands are independent of force, but rapidly the 

resultant adhesion induces the activation of Rac and Cdc42 protein pathways, 

leading to the formation of filopodia and lamellipodia (Figure 7.1). 

These structures create a small adhesion site, called a focal complex (in 

the order of ~1 �m). From this point, cells start to exert traction forces on 

the ECM, with about 0.8–0.9 nN �m �2 being exerted by lamellipodia [10]. 

Filopodia are effectively the “antennae” of the cell, formed at the leading 

edge. Focal adhesions and focal complexes recruit the same core proteins 

[13]; however, focal adhesions are much larger in size and integrins packing 

density, and produce larger forces of a few nanonewton per square 

micrometre [14]. Focal complexes can mature into focal adhesions if there 

is an increase in force at the adhesion site [10, 15, 16], or by the activation 

of the Rho pathway [13]. Thus, physical tension between a cell and the 

ECM appears to be essential for focal adhesion formation and any subsequent 

firm adhesion. 

Finally, it should be noted that cell adhesion, spreading and migration 

require assembly and disassembly of multiple focal adhesions. This is 

regulated by integrin–ligand binding events and can be stimulated by 

properties associated with the ECM (e.g. ligand densities and stiffness 

of the matrix) as well as by intracellular signals [9, 17, 18]. To date, the 

detailed mechanisms that regulate the organisation of these adhesive 

complexes are yet to be elucidated. However, abundant evidence suggests 

a highly dynamic feedback loop between a cell and its microenvironment, 

which is constantly modulated by delicate changes in a vast range of 

(bio)chemical and physical parameters. 

7.2 EngInEErIng tHE ECM For ProbIng 

CEll SEnSIng 

A typical animal cell is �10–100 �m in size. The major components of 

focal adhesion sites, such as integrins, talin and vinculin, are proteins with 

dimensions in the range of several nanometres. Both of these size scales 

require sophisticated tools for visualisation and manipulation of these 

functional components. However, the local microenvironments of cells are 

inherently heterogeneous and dynamically remodelled at different stages 

in the life cycle of a cell. All of these factors can lead to great uncertainty 

and variability in the interpretation of observations. Nevertheless, it is

7.2 ENgINEERINg THE ECM FOR PRObINg CELL SENSINg 199 

because of these challenges that intense effort from many fields has been 

attracted, leading to the combination of micro- and nanotechnology with 

biological sciences and the formation of the interdisciplinary ‘bionanotechnology’ 

field. 

Advances in micro- and nanofabrication can produce precisely controlled 

model systems at a single molecule level, and provide a systematic 

approach to dissect the roles of intertwined parameters in the ECM. In 

combination with other approaches (including optical microscopy, AFM 

and scanning electron microscopy [SEM]), these fabrication methods have 

proven to be powerful in the elucidation of complex cell behaviour. Here 

we will discuss the development of engineered substrates for the investigation 

of cell interactions with the ECM. Specifically, we will review the 

achievements of these substrates in mimicking chemical and physical cues 

in the ECM. Although not explicitly stated in the review below, many of 

these studies described have been underpinned by AFM measurements of 

surface interactions, topography or materials compliance. 

7.2.1 Surface Patterning (Chemical Signals) 

Micropatterning 

Micropatterning is based on photolithography [19], which produces 

features with dimensions over 1 �m. As illustrated in the schematic representation 

in Figure 7.2(A), this process involves the UV irradiation of a 

spin-coated photosensitive polymer layer (photoresist) through a mask. 

UV irradiation through the mask causes the photoresist polymer chains 

to either break up (positive resist) or crosslink (negative resist), leading 

to a difference in solubility between the exposed and unexposed regions 

when immersed in a “developer” solution. After developing, the patterns 

from the mask have been effectively transferred onto the substrate. The 

patterned photoresist can then serve as a protecting layer in subsequent 

processes, such as lift-off to produce metal patterns, or etching to generate 

a relief on the substrate. 

Micropatterning has been extensively used for surface patterning of 

biological molecules. Its main purpose is to allow fine control over the size 

and spatial arrangement of regions that can be specifically functionalised 

for the attachment of ECM proteins. For this, selective immobilisation of 

adhesive molecules on the patterned area is required. It should be noted 

that preventing the physisorption of biomolecules (especially proteins) 

on both the patterned and non-patterned surfaces is equally important, as 

non-specifically adsorbed proteins could also serve as an adhesive region 

for cell attachment. 

A key development in the generation of chemically patterned substrates 

has exploited the formation of self-assembly monolayers (SAM) from 

heterobifunctional organic molecules that bear specific functional groups


(A) 

(B) 

Photolithography 

(a) 

(b) 

(c) 

(d) 

Mask 

Etching Lift-off 

(e) (g) 

(f) 

(h) 

Photoresist 

Substrate 

(a) (b) (c) 

(f) (e) (d) 

Metal 

FIgurE 7.2 Schematic diagram of methods used in micropatterning. (A) Photolithography 

and (B) microcontact printing. In photolithography a mask with opaque and transparent 

features is brought into contact with a substrate coated with a photosensitive polymer (photoresist) 

(a and b). UV light is shone through the mask, exposing the polymer beneath the 

transparent regions of the mask (c). The mask is removed and the resist developed, removing 

either the exposed or unexposed regions of the resist depending on the resist type (d). 

The resist layer can be used as a protective mask during a process to etch the unprotected 

regions of the substrate (e)–(f). Alternatively, metal can be evaporated onto the sample, 

remaining on the regions of exposed substrate after the resist has been dissolved in a ‘lift-off’ 

process (g)–(h). In microcontact printing, a topographically patterned stamp is ‘inked’ by 

contacting it with a sample coated with the desired chemical species (a)–(c). When the inked 

stamp is brought into contact with a clean substrate, the species are deposited on the surface 

in patterned regions dictated by the topography of the stamp (d)–(f).


which react with the substrate. Upon SAM formation, the chemical properties 

of the surface are no longer determined by the underlying substrate 

but by the exposed functional tail groups at the non-substrate end of the 

SAM. A commonly used system is the self-assembled monolayer of an 

alkanethiol (SH(CH 2) nX) on gold; the sulfhydryl head groups (SH–) spontaneously 

form sulphur–gold bonds and leave the functional tail group 

structures (X) tethered away from the surface. The terminal X groups can 

be tailored to have different functionalities [20], e.g., NH 2– and COOH– 

groups for subsequent attachment of proteins or peptides via common 

bioconjugation chemistries [21]. The use of mixed or diluted monolayers 

and tuning the length of the hydrocarbon spacer chain can also be used to 

achieve desired surface properties [22]. SAMs of alkylsilane on hydroxylated 

surfaces of SiO 2/Si substrates, such as glass and silica, have also been 

extensively developed, although here, greater care needs to be taken over 

the reaction conditions to avoid self-polymerisation on the surface. 

As photolithography requires clean room facilities to prevent dust particles 

spoiling the pattern transfer process, the infrastructure costs mean that 

these techniques are often not easily accessible on a regular basis. Thus, a 

pioneering method has been developed by Whitesides’ group, called ‘soft 

lithography’ (microcontact printing, Figure 7.2(B)). This uses a physical 

stamp made from poly(dimethysiloxne) (PDMS) elastomer [23]. The stamp 

is a negative replica of a microstructured substrate (master) made using 

conventional photolithography and/or etching methods. Generally, the 

stamp is fabricated by thermal curing of PDMS against a master template 

followed by peeling away the cured structure. The PDMS stamps can then 

be inked with silanes, alkanethiols or ECM proteins to produce patterns 

on a wide range of substrates [24]. Unstamped regions can be blocked to 

resist non-specific protein adsorption by various methods such as the use 

of PEG-terminated SAMs or rinsing with denatured albumin solution. The 

PDMS stamps can be repeatedly replicated from the master and reused 

many times, thereby significantly reducing the cost of fabrication. Using 

this methodology, microcontact printing has greatly extended the range of 

substrates that can be engineered for use in cell studies since many of the 

polymeric materials compatible with biological studies are not suitable for 

patterning using traditional photolithography processes. 

An early example of the use of micropatterned surfaces is one which 

allowed systematic examination of the interaction of cells with substrate 

surface chemistries and ECM components [25]. Observations of cell 

growth on metallic and polymeric micropatterns have provided invaluable 

information to develop new types of cell culture vessels and screen 

the biocompatiblity of metal materials for implants. Cell function data on 

SAM patterns have enabled the identification of chemistries and systems 

that possess designed properties; e.g. observations from patterns made 

using a range of poly(ethylene glycol) (PEG)-derivatised alkanethiols


(and silanes) have found which exhibit the lowest protein physisorption 

(and hence block cell adhesion) [26–28]. These SAMs can therefore be 

used to form a non-adhesive background. By the integration of specific 

adhesion ligands into these patterns, defined spatial distribution of the 

ligands can be formed, as shown in Figure 7.3(a). Here, a pattern of fluorescently 

labelled fibronectin on a PEG-passivated surface was prepared 

by photolithography. Figure 7.3(b) demonstrates that fibroblasts specifically 

attach and proliferate in the adhesive islands. 

Cellular interactions in vivo are largely varied. Different types of cells 

are juxtaposed in the ECM and each secretes different cues at different 

times. Thus, cells are exposed to temporally spatially regulated concentrations 

or dynamically changing gradients of adhesive cues (e.g. due 

to diffusion of soluble molecules emanating from particular cells). With 

surface engineering being able to tune spatial distances and pattern sizes, 

micropatterning provides a convenient way to study how cells sense 

the spatial distribution of adhesive cues. A study of cells on a micropattern 

of ECM ligands has discovered that the amount of integrin does not 

always determine cell life or death, but instead this is often indicated by 

the degree of cell spreading and its shape [29]. Surface patterning of different 

ligands for two types of cells has also advanced the in vitro study 

100 μm 

(a) 

200 μm 

(b) 

FIgurE 7.3 Example of surface patterning for the generation of adhesive protein patterns. 

(a) Fluorescence-labelled fibronectin patterns on a glass substrate generated using 

photolithography. (b) 3T3 fibroblast specifically attached and growing on the collagen patterns 

but not on the PEG surface between the patterns.


of parenchymal cells such as hepatocytes (liver cells) which require heterotypic 

interactions between non-parenchymal cells (e.g. fibroblast) to 

maintain their liver cell phenotype [30]. In this study, the microfabrication 

approach allowed researchers to specify independent variables, including 

the formation of a heterotypic interface and the ratio of cell populations 

at specific locations in their samples, something which was not possible 

using traditional random co-culture methods. 

Although many of the above findings have been made possible with 

the aid of micropatterning, they have also indicated the desirability of 

further investigation at smaller length scales (�100 nm) where most of the 

molecular mechanisms relevant to cell biology can be discovered. Thus, 

we describe relatively recent investigations that have used nanopatterned 

engineered surfaces in the next subsection. 

Nanopatterning 

To generate nanopatterns, electron beam lithography (EBL) is normally 

used since the spatial resolution of photolithography is limited 

by the diffraction of light. Rather than using a mask, EBL uses a focused 

electron beam to directly write patterns onto an electron beam sensitive 

resist. Since this is a serial writing method, i.e. tracks are written segment 

by segment, this technique can require a significant amount of time to 

write a single large area pattern and is thus very expensive. However, in a 

development similar to the soft lithography described earlier, nanopattern 

structures can also be imprinted onto a solid polymeric substrate (nanoimprinting 

lithography [NIL]), greatly reducing the cost [31, 32]; Figure 7.4). 

By combining NIL with self-assembled monolayer techniques, protein 

nanopatterns of dimension �100 nm have been produced [33, 34]. The 

combined capability of NIL and EBL for the generation of arbitrary nanopatterns 

on a wide range of materials has also led to the discovery of cell 

response to nanotopography, as discussed in later sections. 

Other methods for nanopatterning biological molecules include scanning 

probe lithography [35], self-assembly nanofabrication using block 

copolymer, and colloidal lithography [36]. A good review of these techniques 

is given by Gates et al. [37]. However, to generate a statistically 

meaningful cellular study, fine tailored adhesive nanopatterns have to 

cover a large area, preferably of the order of square centimetre. This 

imposes a big challenge for some of the serial writing methods, such as 

scan probe-associated lithography, although new developments in parallel 

writing using multiple tips might mitigate this barrier. 

As an example of an extension of the self-assembled block copolymer 

technique, recently, Spatz’s group have developed the ‘micelle diblock 

copolymer lithography’. This allows precise control of space between 

RGD ligands at the length scale of 10–200 nm [38]. This strategy uses selfassembly 

of diblock polymer of polystyrene-block-poly(2-vinylpyridine)


Hot 

embossing 

(a) 

(b) (e) 

Heat 

(c) 

(d) 

Heat 

into reverse micelles in toluene which form a uniform thin layer on a 

substrate. The cores of these micelles contain a metal precursor (HAuCl 4) 

that is turned into a regular Au nanoparticle upon oxygen plasma treatment 

of the film. Tailoring the ratios and components of the copolymer 

gives rise to a range of Au nanoparticles of 3–8 nm in diameter with 

spacing adjusted from 15 to 250 nm. By forming these fine Au nanoislands 

on a non-adhesive substrate and subsequent functionalision of the 

(f) 

(g) 

UV 

Flash 

imprint 

FIgurE 7.4 Schematic drawing of nanoimprint lithography (NIL). (a) A master with 

nanoscale topographic features is held above a sample coated in a layer of resist. (b) In hot 

embossing, the resist is a thermoplastic that can be softened with the application of heat. 

(c) The master is brought into contact with the heated resist and held under pressure. 

(d) The heat is removed, and the master is removed after the mask has cooled, leaving the 

topographic features embossed in the resist. (e) In flash imprint lithography, the resist is a 

viscous liquid or soft polymer that can be hardened through UV exposure. (f) The master is 

brought into contact with the resist and held under pressure whilst the sample is exposed 

to UV radiation. (g) The master is removed after the resist has hardened leaving the topographic 

features imprinted in the resist.

Au nanoparticles with a cyclic RGD-thiol, nanoislands of RGD-ligands 

are created. This novel method has enabled a series of studies, demonstrating 

that cells can detect surface variations at the size of a typical protein 

complex (�100 nm) and are affected dramatically by small variations 

in ligand–cluster spacing (e.g. 58 and 73 nm) [39]. 

Although nanopatterning of adhesive molecules is ultimately valuable 

to reveal molecular mechanisms underlying cellular processes, the 

reliability of the information obtained depends on the accuracy of the 

characterisation measurements at the nanoscale. In this context, it should 

be noted that topographic features as small as 10 nm can exert dramatic 

effects on a cell (more details in the next section). This type of observation 

is particularly important for protein nanopatterning studies based on the 

assembly of particle templates, as discussed in Spatz’s work. 

7.2.2 nanotopography 


In contrast to the use of micro- and nanoscale patterns of (bio)chemical 

motifs described earlier, cell behaviour has also been extensively studied 

on patterns of micro- and nanoscale topographic features [40]. 

Motivation for many of these studies comes from the observation that 

although the physical form of the ECM appears as a random meshwork, 

in fact, it contains enormously detailed nano- and microscale structures. 

For instance, a corrugation with a period of 68 nm has been recently 

observed on collagen fibres [41]. When looked at on the small scale, the 

ECM possesses nanopores, micro- and nanofibres, and peaks and depressions. 

Since the middle of the twentieth century, it has been increasingly 

recognised that cells react to microtopography. Early evidence has shown 

that cells adhere, align and move along fibres in the range of 30–100 �m 

[42–44]. In recent decades, the advance in micro- and nanofabrication has 

allowed intense investigations in this area and greatly push forward our 

understanding. 

Since the early 1960s, Curtis and his colleagues have studied the reaction 

of a number of cell types with various microtopographic structures 

[40, 45]. Microgrooves with a wide combination of widths and depths 

have been studied, and it was found that cells react to both depth and 

width. In general, on deep and narrow grooves, cells tend to bridge 

between grooves, whilst on shallow grooves, they often follow the surface, 

although detailed reactions are cell type dependent [46]. Substantial 

evidence has been obtained, showing that adhesion or interaction with 

microscale topographic structures induces changes in cell cytoskeletal 

organisation, apoptosis (programmed cell death), macrophase activation 

(causing inflammatory reactions) and gene expression [47, 48]. The 

observed phenomena clearly demonstrated that microtopography influences 

cell development, and thus triggered researchers to pose questions


about how cells sense the nanoworld, if indeed they can. For example, 

most of the commonly used cell culture dishes have a certain surface 

roughness, does this matter? 

Random or Semi-Random Defined Nanostructures 

The use of spontaneous phase separation of blended polymers or copolymers 

provides an efficient way to produce different nanoscale features 

of controllable depths over a large area [49, 50]. By spin coating blends 

of polystyrene (PS) and poly(4-bromostyrene) (PBrS) onto silicon wafers 

and varying the ratio of polymers and their concentrations, nanoislands 

of heights between 13 and 95 nm were produced (Figure 7.5) and tested 

using fibroblast and endothelial cell cultures [51]. It was found that an 

enhanced cell response was observed on the nanostructured islands 

compared to the planar PS control: 13 nm height islands increased cell 

spreading and proliferation as well as a broad up-regulation of many 

genes involved in proliferation and matrix synthesis [52]. However, 95 nm 

high islands reduce cell spreading and proliferation [51]. Thus, by altering 

only the height of nanoscale features, a different cell response could be 

induced, demonstrating the significant roles that nanotopography might 

exert on cells. 

Although polymer demixing can reliably control the z-depth of nanofeatures, 

there can be less control over the lateral dimensions. In addition, for 

many systems a possible effect from the differences in the chemistry of two 

FIgurE 7.5 AFM picture of an example of nanoislands made by polymer demixing 

process. Image courtesy of Drs. Matthew J. Dalby and Stanley Affrossman.


polymers cannot be completely ruled out. Consequently, an alternative way 

for fast and low cost of fabrication of nanoscale topographic features has 

been sought through the use of colloidal lithography. Monodispersed and 

nanosized colloids made using wet chemistry techniques are commercially 

available. They can self-assemble into a monolayer on a substrate, with the 

spacing between each tailored by their surface charge or functional linker 

groups. The resulting colloid assembly is effectively a ‘photoresist’ pattern 

whose lateral dimensions are determined by the colloid size and spacing. 

Using this approach, nanocolumns of 160 nm height, 100 nm in diameter 

and 230 nm spacing have been produced in a bulk poly(methyl methacrylate) 

(PMMA) polymer [53, 54]. In comparison to the non-structured control, 

nanocolumns reduced focal adhesions of cells, but significantly increased 

density of filopodia formation. As discussed earlier, filopodia formation is 

associated with focal complexes, indicating the involvement of nanotopographic 

features on integrin cluster formation. 

The fact that many of the ECM proteins are present as nanofibres is 

driving intensive research on engineered nanofibres as replacements for 

ECM components. Carbon nanofibre compactions have been investigated 

for osteoblast culture with potential application as orthopedic/dental 

implants [55]. When compared with using conventional carbon fibres 

(diameter �100 nm), osteoblasts proliferate faster and deposit more extracellular 

calcium (indicating osteoblastic bone formation) on the carbon 

nanofibre compactions (diameter �100 nm). In other studies, synthetic 

and natural polymeric nanofibres have also long been regarded as promising 

analogues of the ECM. Here, a vast selection of well-established 

methods can be used to tailor their chemistries to match those found in 

the native ECM. To produce the polymeric nanofibres themselves, electrospining 

has become perhaps the simplest and most efficient technique for 

producing materials which can be assembled into 2D and 3D non-woven 

fibrous mesh (see review by Pham) [56]. Interestingly, cell culture on these 

nanofibre matrixes demonstrated better attachment and increased proliferation 

compared to that on substrates made from larger size fibres. 

Nanofibre meshes have also been found to stimulate cells to develop 

phenotypical behaviour [57, 58]. For example, NIH 3T3 fibroblasts and 

normal rat kidney cells grown on a polyamide nanofibre matrix displayed 

in vivo-like morphology and breast epithelial cells on the same matrix 

underwent morphogenesis into multicellular spheroids [58]. 

All the above-mentioned examples provide evidence which suggest that 

nanotopography has a significant influence on cell adhesion, cytoskeletal 

organisation and morphogenesis. However, the mechanisms involved are 

poorly understood: We do not know whether the less well-defined lateral 

dimensions of nanoislands made by either polymer mixing or colloidal 

lithography play any significant role in cellular behaviour; the nanofibre 

matrix may provide a large surface to volume ratio structure that could


possibly entrap significant amounts of ECM proteins from the culture 

medium; and it is not clear as to what extent the chemistry and texture of 

the nanofibre matrix (or the nanoislands) interact with cells. As a random 

nanophase meshwork with poorly defined ‘nanotopography’ features, it is 

difficult to isolate the many parameters which might affect cells. 

Precisely Defined Nanostructures 

E-beam lithography and associated techniques can produce precisely 

defined nanostructures, so that individual variables can be investigated 

thoroughly. Features as small as 3 nm can be reliably fabricated on a substrate 

[59] and using modern high throughput machines, sufficiently large 

areas can be written for cellular studies. Through combination of EBL 

and NIL techniques, arbitrary nanopatterns can be replicated in thermoplastic 

polymers. Using this method, a large number of replicates having 

identical patterns of designed nanofeatures have been produced on polylactide, 

polycarbonate, PMMA, and polycaprolactone [60–62]. This mass 

production using different materials has enabled direct comparison of the 

influence of substrates having different surface chemistries but the same 

nanotopography on cell behaviour for a number of cell lines. 

The use of arbitrary nanopatterns provides a very flexible and systematic 

way to explore the interactions between cells and the nanoworld, e.g. 

when highly regular arrays of nanopit structures with pit diameters of 35, 

75 and 120 nm were used for fibroblast growth. Within this range of subtle 

variation in pit size, it was found that cell spreading reduced and there 

was less apparent stress fibre formation [60]. Following on from this study, 

EBL was used to create different levels of disorders in the nanopatterns. 

Using these levels it has been found that human mesenchymal stem cells 

(MSCs) were prompted to produce more bone mineral when there was 

a certain degree of disorder to the array patterns of nanopits (Figure 7.6; 

[61]). However, highly ordered nanopits resulted in low to negligible cellular 

adhesion and osteroblast differentiation. This discovery suggested 

that nanotopography might be an efficient method to guide MSC cells to 

be used in regenerative medicine and tissue engineering devices, since at 

present, many examples of failed bone implants have been found to be 

associated with encapsulation by soft tissue without direct bone bonding. 

Clearly, substantial studies have advanced our understanding of the 

influence of topography on cellular processes. However, it is still to be 

resolved as to how cells detect and respond to these nanofeatures. Much 

evidence has shown that nanotopography influences cellular cytoskeleton 

formation, and thus is likely to modulate membrane receptor organisation, 

integrin cluster formation, and intracellular signalling – all of which are 

related to focal adhesion formation. It is not clear as to whether the mechanosensitivity 

of cells to physical topography features employs the same 

machinery that cells use to sense changes in surface chemistry (e.g. adhesive 

patterns). New investigations have started to understand the changes


Ordered pattern 

(a) (d) 

(b) 

200 μm (e) 

(c) 

1 μm 

200 μm 

in signalling and genetic analysis. With ever closer collaboration between 

biologists and engineers and the availability of advanced tools for nanoscale 

measurements, such as AFM, a greater understanding of the underlying 

mechanisms of cellular interactions will be possible. This will lead to the 

development of more effective methods for regenerative medicine. 

7.2.3 nanoscale Measurement: Challenges and 

opportunities for AFM 

It might have not been possible to discover many of the findings 

related to nanotopography-induced cellular reactions without the AFM. 

AFM imaging permits reliable and routine characterisation of nanotopographic 

features with high resolution particularly in the z-direction, 

(f) 

Disordered pattern 

FIgurE 7.6 The effect of nanotopography on cell differentiation. SEM images of nanotopographies 

fabricated by EBL (a and d). The nanopits (120 nm diameter, 100 nm deep) 

arranged in a highly ordered square (a) and with each pit randomly displaced from the 

square pattern (�50 nm from the true centre) (d). The disordered nanostructures stimulate 

the human MSCs to express the bone-specific ECM protein osteopontin, as shown in 

(e and f) (arrows) in contrast to no effect seen with the highly ordered pits (b and c). Figure 

reprinted from Dalby et al. [61] with permission.


facilitating the discovery of the significant effects on cell behaviour with 

subtle variations in the height of the nanoislands (13–95 nm) as described 

earlier (Figure 7.5). It has also long been desirable to image both 

nanoscale functional cellular components and nanostructures simultaneously. 

In the past, biologists have employed SEM and immunostaining 

transmission electron microscopy (TEM) approaches to observe functional 

proteins (such as vinculin). However, these approaches require 

many steps of sample preparation, including cell fixing, immunostaining, 

sample drying, and thus many features can be disguised. Although AFM 

has been a powerful tool in the study of isolated biomolecular systems 

and their interactions, only more recently have nanoscale observations of 

living cells been achieved. The rapid expansion of the AFM approach to 

living cell studies has just started. 

Many biological processes involve forces, and this is very much the case 

for cells adhering to the ECM. However, quantification of these forces is 

not straightforward, because a whole cell produces only small forces in 

the nanonewton range. Furthermore, the dimensions of functional components 

of a cell range from subnanometre (nucleic acid) to micrometre 

(whole cells), and measurements can be complicated by the whole cell 

structure dynamically remodelling during cell activities [14]. AFM with 

the ability to measure forces as small as piconewton and distances �1 nm 

demonstrates great flexibility and versatility for investigating the mechano- 

physical events occurring during biological interactions ranging from 

those of a single nucleic acid (deoxyribonucleic acid [DNA]) to those associated 

with whole intact cells. 

AFM in conjunction with the colloidal probe techniques has further 

broadened its applications. Here, there are vast combinations in the choice, 

designs and functionalisation of probes, allowing a range of studies from a 

single biomolecular interaction to cell or polymer mechanics. The discovery 

that a cell exerts force on a substrate, as mentioned earlier, has initiated 

significant efforts to investigate the role of mechanical properties in 

cell activities. In this context, the AFM microsphere indentation technique 

has provided an assessment tool with high sensitivity and microscale resolution 

that can perform well-defined investigations into cell interactions 

with substrates of different elasticity. In pioneering studies in this field it 

has been found that cell growth, differentiation, spreading and migration 

are all regulated by the elasticity of the substrates [63, 64]. 

As AFM is a surface-based technique with high resolution, the integration 

of AFM with optical microscopes is essential for the investigation of 

intracellular events during scanning. There have been long standing questions 

about the dynamics of structural adaptations of a cell in the context 

of mechanotransduction [65]. For example, how do cells use their cytoskeleton 

conformation to transduce a mechanical stimulus to the nucleus and 

induce genomic variations? Frequently, there are also many requirements

for in situ monitoring of changes in intracellular signalling in combination 

with cellular physical variations as a result of the presence of drugs. These 

are most readily revealed by optical fluorescence assays. Consequently, in 

the last few years, instrument manufacturers have developed a number 

of combined AFM-optical microscope platforms that are now starting to 

benefit studies in the fields of bioengineering, cell engineering and basic 

cell biology. In particular, configurations involving confocal microscopy 

[66] and total internal reflection fluorescence microscopy [67] have already 

demonstrated their power in in situ living cell studies. 

Since the invention of the AFM in 1986, we have witnessed significant 

growth of the employment of AFM to probe biological systems. In the 

next section we focus on recent developments associated with intact cell 

measurement. 

7.3 AFM In CEll MEASurEMEnt 

The unique advantages of AFM in cell measurement lie in its capability 

of being able to simultaneously (1) image cell topology under nearphysiological 

conditions, (2) measure mechanical properties of living 

cells, and (3) monitor functional cellular components and intracellular 

processes in conjunction with optical microscopy. This section will demonstrate 

the great potential of AFM for investigating the interaction of 

cells with their environment. 

7.3.1 AFM Imaging of Cells 

7.3 AFM IN CELL MEASUREMENT 211 

In the early days of AFM imaging of cells, the main restriction was 

the limited scan size of the instruments [68], due to cells being relatively 

large structures. As soon as the first instruments with scan ranges of several 

micrometres were developed, they were deployed to image cells [69]. 

Today, modern bio-AFM instruments integrate an AFM platform onto the 

stage of a conventional inverted optical microscope, thus enabling easy 

positioning of AFM tip over a particular region of cells (Figure 7.7(a)). 

This development has been very useful in identifying regions of interest 

in cell morphology and where cells react to the microstructured substrate 

(Figure 7.7(b)). In addition, the optical imaging also permits simultaneous 

monitoring of the lateral morphology of cells and/or intracellular 

signalling during the investigation by AFM [70]. Through a ‘direct overlay’ 

technique, it is possible to integrate AFM with optical images and 

use the optical image to guide AFM operation. This enables correlation of 

the biophysical and biochemical functionalities of a cell. In reality, the different 

operating principles of AFM and optical microscopy can result in


(a) (b) 

FIgurE 7.7 Optical images of an AFM cantilever positioned over a cell on (a) a planar 

substrate and (b) a structured substrate. 

an inaccurate overlay of the two images; however, this can be overcome 

by the use of registration methods devised by the manufacturers [71]. 

In many studies, fixed cells have been used to preserve cell morphology 

and maximise the imaging resolution with functional intracellular 

structures being revealed by staining. AFM and fluorescence images of 

an osteoblast cell cultured on a nanopatterned polycarbonate substrate 

prepared by EBL and NIL as described in an earlier section are shown in 

Figure 7.8. Although fluorescence images of the F-actin (light colour in 

Fig. 7.8(a)) and tubulin (light colour in Fig. 7.8(b)) elements within a cell 

protrusion already suggest a well-developed cytoskeleton structure, the 

AFM images reveal incredible details of the cell structure (Figure 7.8(c)– 

(f)). Both the well-spread straight actin stress fibres and the more curved 

tubulin network are visible. Here, the AFM image measures the height 

of the cell structures with a resolution that could not be obtained using 

techniques such as confocal microscopy. As is common practice with biological 

cell measurements, AFM data are recorded in two image channels: 

the height image shows an overall topography and the error signal image 

highlights nanometre-scale surface topography, revealing well-defined 

variations in the structure. As a cautionary note, it should be noted that 

although the fixing procedure eases AFM imaging, it can also cause damage 

and alteration of delicate cellular structures [72]. 

Living cells, although more relevant to studies of most biological events, 

are one of the most challenging samples to image with AFM [73]. They 

are much softer than fixed cells and often react to the imaging process 

itself – sometimes retracting filopodia or excreting vesicles. Some cell types, 

e.g. fibroblasts are harder to image than others due to their restless nature

Slow (μm) 

40 

20 


(a) (b) 

0 

0 20 

Slow (μm) 

(e) 

Fast (μm) 

(c) (d) 

8 

6 

4 

2 

0 

40 

0 2 4 6 8 

Fast (μm) 

645.5 nm 

0 nm 

183.3 nm 

0 nm 

under the tip, and the height contours of some are so steep as to prove 

difficult for the AFM tip to follow topographically. Thus, there are many 

considerations to take into account when designing experiments using 

live cell imaging, such as operation modes, loading force, choice of tip 

Slow (μm) 

Slow (μm) 

(f) 

40 

20 

8 

6 

4 

2 

0 

0 

0 20 

Fast (μm) 

0 2 4 6 8 

Fast (μm) 

129.7 mV 

0 mV 

309.1 nm 

FIgurE 7.8 Simultaneous AFM and optical imaging of functional cell structures on a 

nanostructured substrate. Fluorescence images show an overview of the F-actin stress fibres 

(light colour in (a)) and tubulin (light colour in (b)) cytoskeleton protein distributed on a protrusion 

region (a and b). AFM height (c) and error images (d) revealing the detailed subcellular 

structures of the same region. The Directoverlay TM feature (JPK instrument Ltd) was 

employed for image overlay and positioning of the AFM tip, permitting precise location of a 

zoomed in region (identified in d). AFM images (e and f) of the zoomed in region, revealing 

the filopodial interacting with the underlying nanopatterned structures. AFM imaging was 

carried out in contact mode using a silicon nitride cantilever with spring constant 0.01 N m �1 . 

40 

0 mV


and appropriate physiological conditions (medium temperature and pH). 

Although advances in cell immobilisation and AFM imaging modes now 

permit soft, live cells to be imaged, the process remains far from trivial [74]. 

For living cell imaging, an environmental control chamber with suitable 

medium is essential to keep cells alive and viable. When imaging 

in contact mode, cantilevers with the lowest spring constants (0.003– 

0.06 N m �1 ) operating with a small loading force (�1 nN) are preferred. 

Following these basic considerations, it is possible to successfully image 

live cells. Figure 7.9(a)–(f) show height and error images of live 3T3 cells 

on a fibronectin-coated glass slide and a fibronectin-coated PDMS microgrooved 

substrate. A well-spread cell morphology with fibrous cytoskeleton 

structures can be seen clearly in Figure 7.9(a) in comparison to the 

restrained morphology of the cell on a flat PDMS substrate (Figure 7.9(c) 

and (d)). This can be further demonstrated by quantitative analysis of the 

cell height and its projecting area. It should be noted that cells tend to 

detach from the PDMS substrates during imaging. All of these observations 

demonstrate that 3T3 fibroblasts have much weaker adhesion to 

soft PDMS substrates. On microstructured PDMS structures, cells tend 

to position their nucleus in the trough of the channel, close to one edge 

and mostly attach filopodia to the upper surfaces (Figure 7.9(e) and (f)). 

This gives rise to a preferred cell alignment along the channel length, as 

discussed earlier. Thus, AFM imaging provides a quantitative and high 

resolution approach to studying the behaviour of living cells. 

7.3.2 Elasticity Measurement of living Cells 

On a soft sample surface, an approaching tip with controlled force will 

cause an indentation. Although this is often problematic for AFM imaging 

of living cells, it is a way to measure and map the elastic properties 

of the cell structure. For a force–distance measurement, the deflection of 

the cantilever is plotted as function of the z-separation of the probe and 

the sample. On a stiff sample (e.g. glass), the deflection is proportional 

to the probe sample separation. However, on the soft sample, the movement 

of the tip will be less than that of the sample, and the difference is 

the indention of sample (Figure 7.10(a)). 

In order to be able to extract material properties from an AFM force– 

distance curve, we must interpret the deflection using an appropriate 

model. As a starting point, it is reasonable to consider an AFM force– 

distance curve as arising from a conical tip indenting a planar surface. 

This was first considered by Hertz in 1882 [75] (equation (7.1)) and later 

generalised by Sneddon [76]. 

F � � 

2 

2 E 

⋅ ⋅ 

π 

2 

1 � v 

( ) 

⋅ ( �) 

tan 

(7.1)

Slow [μm] 

(a) 

Slow [μm] 

(c) 

Slow [μm] 

(e) 

100 

50 

0 

0 50 

Fast [μm] 

80 

60 

40 

20 

0 

0 50 

100 

20 

Fast [μm] 

0 

0 20 

Fast [μm] 

40 


718 nm 

0 nm 

2.774 μm 

0 μm 

7.749 nm 

0 μm 

This model has subsequently been applied to AFM data by many 

researchers [77, 78] and modified to account for a number of tip geometries 

[79]. In order to use the Hertz model to calculate the Young’s 

modulus (E) of a sample, several experimental parameters have to 

be known: the applied force (F), indentation depth (�), semi-opening 

Slow [μm] 

(b) 

Slow [μm] 

Slow [μm] 

(f) 

100 

50 

0 

0 50 

Fast [μm] 

80 

60 

40 

20 

0 

0 50 

40 

20 

Fast [μm] 

0 

0 20 40 

Fast [μm] 

428.7 mV 

0 mV 

2.038 V 

0 V 

1.375 V 

FIgurE 7.9 AFM images of living cells on different substrates, glass (a and b), flat 

PDMS (c and d) and a microgrooved PDMS substrate (e and f). The grooves in (e) and (f) 

have a 12.5 �m period and are 1 �m deep. All the substrates were coated with fibronectin. 

(d) 

0 V


(a) 

On glass 

On nucleus 

On filopodia 

0.0 

–1400 –1200 –1000 –800 –600 –400 –200 0 200 

Piezo-displacement (nm) 

(b) 

angle of the tip (�, only for a conical tip) and Poisson’s ratio (v, normally 

assumed to be 0.5 as cells are virtually incompressible). Young’s 

modulus can then be calculated by taking � and F at a single point or 

by fitting to the contact region of a force distance (F–�) curve. In the 

single-point method, a significant uncertainty comes from the accuracy 

of determining the point where the tip first contacts the surface with zero 

force (contact point). This can be extremely difficult, and so it is normally 

recommended to fit the data in the contact region. 

δ 

d 

0.4 

0.3 

0.2 

0.1 

δ 

Force (nN) 

δ 

Contact point 

δ + d 

FIgurE 7.10 Schematic diagram showing indentation of a soft substrate by an AFM tip 

and cantilever (a). Contact point between the tip and substrate with no load or indentation 

of the sample (left image). Tip indenting the sample by a distance �, with a load caused by 

the cantilever deflection d, the total displacement of the tip–sample separation is given by 

� � d (right image). Examples of force curves generated on a solid glass substrate (no indentation), 

a cell nucleus region and a filopodia region (b). Note the heterogeneity of the cell. 

The indentation distance into the sample (�) can be corrected by subtracting the cantilever 

deflection (d) from the piezo-displacement.

7.4 CONCLUSIONS 217 

In using simple Hertz-based models, it is important to realise that they 

may be valid only for small indentations, in the region of 5–10% of the total 

sample depth. In the case of cells, this will result in the first 200–500 nm 

of indentation giving a valid fit, but at deeper indentations the underlying 

substrate will start to influence the data. To overcome this problem, there 

has been some work on models that can accommodate indentation deeper 

than 10% of the total sample thickness [80], although currently they are not 

as well established as the conventional Hertz model. 

Other considerations that should be taken into account when measuring 

the mechanical properties of cells include the inhomogeneity and non-elastic 

nature of a cell. For example, the indentation of cell nucleus and filopodia 

is quite different as shown in Figure 7.10(b). Although it is assumed 

that the cell is truly elastic for the purpose of data analysis, some of the 

energy delivered during indentation will be dissipated due to the viscous 

and slightly plastic nature of a cell. This effect can be seen in the velocity- 

dependent hysteresis that can be observed in some experiments [78, 81]. 

Measurements may also vary between cells, or even on the same cell due 

to the internal components of cell moving beneath the indenting tip. 

Since Tao et al. first utilised AFM for quantitative measurement of local 

elastic properties of a biological sample (cow tibia) [82], there has been 

significant growth in the use of AFM for elasticity measurements of living 

cells [83–86]. It has been found that the elasticity (or stiffness) of different 

cell types can vary from 0.1 to 40 kPa [87], and cell elasticity might 

function as a quantitative indicator during cell differentiation. Many studies 

have also shown that cancer cells are substantially softer than normal 

cells [88, 89], indicating that quantitative analysis of mechanical properties 

could be used to differentiate between cancerous and normal cells 

with similar appearances. The quantitative information of local cell elasticity 

in nanoscale spatial resolution has also provided valuable insights 

into cellular processes such as cell spreading [90] and cell migration [91]. 

Monitoring the change in elasticity while treating cells with drugs that 

disrupt specific cytoskeletal structures (i.e. F-actin, tubulin and intermediate 

filaments) reveals that the actin network mainly determines the elastic 

properties of living cells [66]. Apart from the continuous contribution to 

understanding fundamental cellular mechanisms, these developments are 

also promising for drug testing studies [92]. 

7.4 ConCluSIonS 

Recent developments in micro- and nanoengineering have created 

many opportunities to investigate the complex processes in cellular biology. 

Engineered surfaces with micro- or nanoscale features, either chemical


or physical in nature, have been reliably produced by various methods. 

Many of these structures have emerged from the novel combination of 

advances in micro- or nanofabrication, chemistry and biology. Surface 

patterning methods offer considerable flexibility in pattern design, ligand 

specificity and density, and surface composition to investigate interactions 

of cells with chemical variations in the ECM. A vast range of engineered 

topographic features, from micro- to nanoscale, have been found to play a 

significant regulatory role in cellular proliferation, migration and differentiation. 

These studies provide significant insights into mechanistic questions 

of how cells are able to sense, integrate and respond to collective 

chemical and mechanical signals. In addition, they also demonstrate that 

engineered environments can regulate cell functions and fate, and thus 

open new opportunities of developing tailored biosubstrates for specific 

tissue cell types, although this is still at its early stage. 

Optical microscopes and SEM have been essential tools for many of 

these studies; however, they are subject to many constraints in exploring 

the molecular mechanisms at subcellular or cellular level, which are essential 

for the control of the biological pathway. AFM, having been established 

as an important tool in development of nanopatterned surfaces, 

has provided increased momentum to living system studies. Nanometre 

spatial imaging and quantitative measurement of mechanical properties 

of functional components of a living cell have been reliably achieved. 

Long standing questions in the nanoworld, such as whether it is nanoscale 

topographic features or chemical patterns that predominate in inducing 

cellular reactions [40], may be answerable. The combination of AFM 

with existing optical techniques has already shown itself to be a powerful 

tool, and further insights will be gained into in vitro cell differentiation and 

disease diagnostics. Together with the engineered environments that can 

be employed to guide cell function and fate, it might be possible to move 

towards controlling biological pathways in cell culture, and so explore new 

medicines and therapies for human health. 

There are still many open challenges in cell biology and in physiological 

and pathological dysfunctions. The convergence of micro- or nanoengineering, 

AFM and interfacial chemistry with cell biology tools might 

provide new opportunities to address these challenges. For example, a better 

understanding of the complex processes associated with a whole intact 

cell interacting with individual molecules when cells are in contact with a 

surface will facilitate the diagnostics of arthoroplastic failures and improve 

existing implants. A more ambitious approach is to regenerate failed tissue 

outside a body; this requires an engineered ECM with the functionalities 

that are found in a body. Although there have been intensive efforts in 

these fields, researchers are still a long way from recreating an ECM with 

similar molecular architecture and functionalities of the ECM found in vivo.

AbbREvIATIONS ANd SyMbOLS 219 

Increasing collaborations between scientists and communities from various 

disciplines, including engineering, nanobiotechnology, materials, biology 

and clinical medicine, are essential to approach this goal. 

ACknowlEdgEMEntS 

H. Yin is supported by the Royal Society of Edinburgh as an RSE personal 

research fellow. G. McPhee thanks the EPSRC for his studentship. 

P. S. Dobson is supported by an RCUK Academic Research Fellowship. We 

would like to thank Dr Matthew Dalby for proof reading and offering constructive 

suggestions and samples. We also thank Drs Andrew Glide and 

Mathis Riehle and Professor Jon Cooper for their support and discussions. 

AbbrEvIAtIonS And SyMbolS 

� Semi-opening angle of the tip ° 

AFM Atomic force microscope 

DNA Deoxyribonucleic acid, a nucleic acid 

E Young’s modulus N m�2 EBL Electron beam lithography 

ECM Extracellular matrix 

F Applied force N 

MSCs Human mesenchymal stem cells 

NIL Nanoimprinting lithography 

PBrS Poly(4-bromostyrene) 

PDMS Poly(dimethysiloxne) 

PEG Poly(ethylene glycol) 

PMMA Poly(methyl methacrylate) 

PS Polystyrene 

RGD A peptide sequence consisting of 

Arg-Gly-Asp 

SAM Self-assembly monolayer 

SEM Scanning electron microscopy 

TEM Transmission electron microscopy 

V Poisson’s ratio, dimensionless 

� Indentation depth m


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C H A P T E R 

8 

Atomic Force Microscopy 

and Polymers on Surfaces 

Vasileios Koutsos 

O U T L I N E 


8.2 Basic Concepts 227 

8.3 End-grafted Polymer Chains 229 

8.4 Diblock Copolymers Adsorbed on Surfaces 236 

8.5 Star-shaped Polymers Adsorbed on Surfaces 237 






8.1 IntroDuCtIon 

The surfaces of materials are routinely modified with coatings to protect 

them in hostile conditions and to functionalise them for a variety of 

purposes. Polymer coatings play an important role in such modifications. 

Polymer synthetic chemists are nowadays able to produce a huge number 

of different macromolecules of controlled structure and composition 

(and consequently function) in large quantities and at a relatively low cost. 

Furthermore, polymers are usually processed readily and inexpensively. 



226 8. ATOMIC FORCE MICROSCOPy ANd POLyMERS ON SURFACES 

Ultrathin polymer coatings, in particular, play a crucial role in many 

processes, ranging from decoration and protection against a variety of 

degradation agents (corrosion/chemical) [1] to microfabrication methodologies 

for microelectronics [2] and biomedical devices [3]. In all situations, 

at the polymer-solid interface, there is a layer of polymer chains 

that are in direct contact with the solid surface. The coating can be so 

thin that it actually consists of just one mono-macromolecular layer, i.e. 

a monolayer of polymer chains that are all in contact with the solid surface. 

Such monolayers are typically some nanometres thick (the thickness 

is of the order of the typical size of one polymer chain). In many 

cases, the solid surface is not fully covered with polymer chains, and we 

have the formation of a submonolayer, the structure of which can range 

from a complete layer occasionally disrupted by some isolated holes to 

a solid surface only partially covered by some isolated polymer islands. 

Depending on the molecular interactions and the number of chains at 

the surface (surface coverage), there is a variety of different continuous, 

semi-continuous and discontinuous nanopatterns and nanostructures 

that can be formed. 

Polymer monolayers and submonolayers on solid surfaces play an 

important role for many technological applications such as nanopatterning 

and surface modifications used in microelectronics [4], colloidal stability 

and flocculation [5], polymer reinforcement with nanofillers [6, 7], 

non-fouling biosurfaces [8], biocompatibility of medical implants [9], 

separations [10], microfluidics [11], adhesion, lubrication and friction 

modification [12]. Of particular importance are recent developments in 

the direction of achieving smart responsive surfaces to various external 

stimuli using polymer monolayers and nanostructures [13–15]. 

The atomic force microscope (AFM) [16] provides a spatial and force 

resolution in the order of angstroms and tens of piconewtons, respectively; 

therefore, it is ideally suited to study the fine morphology and 

physico-chemical properties of materials at the nanometre scale, directly 

in real space. This is of particular importance in the field of polymer- 

modified material surfaces. The traditional surface techniques lack the 

lateral resolution at the nanometre scale, which is necessary in order 

to analyse laterally inhomogeneous monolayers and submonolayers of 

polymers, macromolecular-size clusters and polymer nanostructures or 

nanopatterns. Furthermore, the AFM can operate under liquid conditions, 

providing a direct look of polymers anchored on surfaces in various 

solvent conditions. In many cases, solution-based processing techniques 

(e.g. dip-coating, spin-coating, droplet-evaporation, spraying) are employed 

and consequently, direct measurements within a good solvent (for the 

polymer) are of particular importance. AFM investigations within liquids 

can reveal and elucidate the physico-chemical phenomena governing 

the polymer monolayer behaviour during formation and processing.

8.2 BASIC CONCEPTS 227 

Fur-thermore, in many cases, mainly within biotechnology applications, 

the functional use of the polymer monolayer is under liquid (e.g. aqueous) 

conditions and in these cases AFM provides the opportunity for direct, 

real-space and real-time monitoring of the polymer layer during its functional 

role. In any case, it has to be noted that AFM studies of dry polymer 

monolayers are more numerous since they are easier to implement. To 

some extent, they can provide important snapshots of polymeric behaviour 

in the solution and can elucidate many aspects of the polymer behaviour. 

In this chapter, first, a concise and simplified version of the fundamental 

physical ideas of how polymer chains behave when they are in close 

proximity to surfaces is presented; the following part is dedicated to the 

main objective of this chapter, which is to demonstrate the potential, versatility 

and flexibility of the AFM technique to probe in a direct manner 

the nanoscale structural and physical properties of polymer monolayers 

and submonolayers. To this end, we use some selected examples from 

our own AFM studies. We show that the structural regimes depend on 

many factors such as surface interactions, polymer molecular weight, 

surface density, solvent conditions, chemical composition and molecular 

architecture. The structural properties of these ultrathin polymer films 

have a profound effect on various chemomechanical properties of the 

modified surfaces. 

In summary, we show in a direct manner the important role of the 

AFM as a very appropriate characterisation technique and tool for the 

investigation of materials surfaces that has been modified and processed 

by polymer monolayers and submonolayers. 

8.2 BASIC ConCEPtS 

A polymer chain can be attached on a surface by physical (e.g. van der 

Waals, electrostatic forces) and chemical (e.g. covalent) bonds. Its behaviour 

depends strongly on the characteristics of the attachment such as the 

number and position of attachment points (e.g. anchoring by its end or 

attachment points along the backbone of the chain) and bond strength, 

with chemical bonds being usually stronger than any physical attractive 

forces and hydrogen bonds (which are ranked as of moderate strength). 

One has to note that a large number of weak physical bonds can be a very 

efficient way of attachment and in this way a polymer chain can take a 

flat conformation (Figure 8.1). Nevertheless, the adsorption by chemical 

bonds (chemisorption) is considered irreversible, while adsorption by 

physical attractive forces (physisorption) is usually reversible under certain 

processing conditions. 

A polymer chain in good solvent conditions (e.g. polystyrene in toluene) 

is swollen since the polymer segments repel each other because of the


Tails 

Loops 

(a) (b) (c) 

FIgurE 8.1 (a) A polymer chain chemically attached by one of its ends to a solid surface 

‘swollen’ in a good solvent. (b) A polymer chain physisorbed on a solid surface by nonspecific 

(physical) interactions along its backbone (four contact points), forming three loops 

and two tails. (c) Diblock copolymer in a solvent attached on a solid surface by adsorption 

of one of its two blocks. 

repulsive excluded volume interactions between the monomers. If the 

solvent conditions change to bad (e.g. polystyrene in water or in dry state), 

then the polymer chain collapses into a dense globule as the monomer- 

monomer attractive forces prevail and the polymer tries to minimise its 

contact area with the unfavourable solvent (Figure 8.2a, b). If the polymer 

chain happens to be attached on the surface, the behaviour is similar 

(Figure 8.2c,d) but the final conformation is to be affected by the strength 

of monomer-surface interactions and location of the attachment points. An 

isolated end-grafted polymer chain with negligible interactions (apart from 

the end-grafting) with the solid surface resembles a mushroom (especially 

when it is swollen in good solvent conditions), and for such grafting densities, 

the polymer chains are within the ‘mushroom’ regime (Figures 8.1a 

and 8.2b,c). In contrast, if the polymer-surface interactions are high enough 

and involve very many polymer segments, the polymer takes a flat conformation, 

which resembles a pancake, signifying the ‘pancake’ regime. 

If the grafting density is high enough, the polymer chains start to 

overlap and interact with each other, and consequently the whole polymer 

layer can increase its thickness (compared with the dimensions of 

a single polymer chain in the corresponding solvent conditions). This 

effect is particularly dramatic in good solvent conditions since in this 

case the excluded volume interactions between the polymer segments 

are repulsive and the whole polymer layer is stretched away in the perpendicular 

to the solid surface direction, as depicted in Figure 8.3(a). For 

sufficiently high grafting densities, the polymer layer resembles a brush 

[17] and it is called a ‘polymer brush’. What will happen to the morphology 

of such polymer monolayers upon drying? Will the polymer chains 

collapse individually or in a homogeneous layer or even in aggregates 

(Figure 8.3)? Could one use such a process to form useful nanostructures 

and nanopatterns? Furthermore, what is the effect of polymer composition 

or polymer architecture and what are the nanomechanical properties 

of such polymer layers?

(a) 

Good solvent: 

swollen state 

8.3 ENd-gRAFTEd POLyMER CHAINS 229 

(c) (d) 

Bad solvent: 

collapsed state 

FIgurE 8.2 (a) A swollen polymer chain in the ‘bulk’ solution and (b) in a collapsed 

globular state upon the change of the solvent conditions from good to bad. (c,d) The same 

transition for an end-grafted polymer chain with negligible affinity for the solid surface 

(mushroom regime). 

In the following sections, we will be demonstrating the AFM capability 

to give answers to these and other similar questions using specific examples 

of chemisorbed or physisorbed polymer chains on solid surfaces from 

dilute polymer solutions. Owing to the characteristic nanometre-scale size 

of single chains and thickness of polymer monolayers, any inhomogeneity, 

aggregation, instabilitity and dewetting effects of such layers can be 

readily and directly probed by atomic force microscopy, which is based on 

piezoelectric transducers and sharp probing tips mounted on microfabricated 

cantilevers that scan the interrogated surface and are simultaneously 

monitored by the laser beam deflection technique while a feedback loop 

controls the distance between the probing tip and sample. 

8.3 EnD-grAFtED PoLymEr ChAInS 

An efficient way of attaining purely end-grafted polymer chains is to 

use thiol-terminated macromolecules, i.e. polymer chains ending in –SH, 

and gold substrates. In this case, one achieves a quite strong chemical bond 

(b)


(a) 

(b) 

FIgurE 8.3 Schematic drawing of a polymer brush in (a) good solvent conditions and 

(b) poor solvent conditions. Upon the change of the solvent conditions, the polymer chains 

could self-organise in nanoscale aggregates of small groups of polymer chains instead of 

collapsing individually. 

between the thiol and gold, end-grafting the chain, while its backbone is 

not affected by the inert Au surface (negligible physisorption). A system 

based on several molecular weights of various thiol-terminated polymers 

chemisorbed on gold substrates from dilute solutions at different incubation 

times was used in order to investigate the different structural regimes 

of such end-grafted polymer monolayers and submonolayers [18–20]. The 

gold substrates were immersed in the polymer solutions for a designated 

duration and upon removal from the solution were rinsed exhaustively 

with fresh toluene and subsequently dried under a stream of argon. The 

AFM imaging was performed in water in contact mode at very low force 

set-point; capillary forces were avoided since both the sample and the 

cantilever/tip were immersed in water. 

In Figure 8.4, we show a three-dimensional AFM topography map 

of a gold substrate sample prepared by immersion in a toluene solution 

of thiol-terminated polystyrene, PS-SH (concentration 0.1 mg ml –1 , 

weight-average molecular weight M w� 144 000 g mol –1 ), for 45 min. It 

was imaged by AFM in water (bad solvent for PS). The gold substrate 

morphology of flat gold terraces separated by valleys and channels can 

be observed, while well-separated globular polymer islands on top of the 

terraces can be clearly seen. 

Although the height of the polymeric islands can be deduced directly 

from AFM topography images, their lateral size is usually overesti- 

mated owing to the convolution between the volumes of the tip apex 

and the polymeric island. One can employ deconvolution methodologies

1000 nm 


500 nm 

0 nm 0 nm 

500 nm 

24.95 nm 

1000 nm 

FIgurE 8.4 AFM 3D-graph topography image of a gold substrate immersed in a toluene 

solution of PS-SH (concentration: 0.1 mg ml –1 , molecular weight: 144 000 g mol –1 ) for 45 min. 

The AFM imaging was conducted in water, which is a bad solvent for PS. The polymer chains 

are in collapsed globular state and randomly distributed on the gold terraces. 

including simple geometrical formulas in order to estimate the true volume 

of the islands [18, 20]. The dimensions of polymer islands deduced 

directly from AFM images show an average height and width of about 

5.5 and 48 nm, respectively. As we have explained, although the measurement 

of height can be reliable, the width is usually overestimated 

owing to the convolution effect. Assuming that the shape of a polymer 

island is a spherical cap and taking into account the convolution effect, 

the average volume of the globules was estimated to be around 310 nm 3 . 

This compares well with the volume of a single collapsed polymer chain, 

which can be calculated assuming the usual bulk density for polystyrene 

(�1 g cm –3 ). Therefore, we conclude that the polymer islands are isolated 

single polymer chains chemisorbed and collapsed into dense globules 

onto the gold substrate. This implies that for this incubation time the 

polymer chains are sparsely distributed and the grafting density is low 

enough for us to observe the ‘mushroom’ regime. The variation in the 

size of the polymer globules reflects the polymer polydispersity (M w/ 

M n� 1.2, where M n is the number-average molecular weight) and possibly 

small changes in the globular conformation, which can be magnified 

by the convolution effect. 

Figures 8.5 and 8.6 show two examples of gold substrates that 

were immersed in a toluene solution of higher concentration of PS-SH 

(2 mg ml –1 ) for much longer incubation times (2 days) and imaged under 

water in contact AFM mode. We can clearly see that the gold substrates 

are covered by a dense array of large polymer globules. Forty-eight hours 

is adequate time for the adsorption to reach its maximum grafting density, 

and we expect to have several thousands of chains within a square


1000 nm 

500 nm 

0 nm 0 nm 

500 nm 

34.56 nm 

1000 nm 


solution of PS-SH (concentration: 2 mg ml –1 , molecular weight: 258 000 g mol –1 ) for 48 h. 

The AFM imaging was conducted in water, which is a bad solvent for PS. The polymer 

chains form aggregates (pinned micelles) on the gold terraces. 

1000 nm 

500 nm 

0 nm 0 nm 

500 nm 

29.25 nm 

1000 nm 


solution of PS-SH (concentration: 2 mg ml –1 , molecular weight: 51 500 g mol –1 ) for 48 h. 

The AFM imaging was conducted in water, which is a bad solvent for PS. The polymer 

chains form aggregates (pinned micelles) on the gold terraces. 

micrometre area. The globular islands are too many and too large in size 

to be individual collapsed chains. 

Since for sufficiently long incubation time we expect to be close and 

above the overlap grafting density, the polymer chains are too close with 

each other to collapse separately. Instead, they collapse fusing together in 

small clusters, the size of which is moderated by the grafted tethers. They 

form aggregates connected to the surface through the tethers; these structures 

have been called ‘pinned micelles’ or ‘octopus surface micelles’ and 

they have been predicted by theory [21, 22].

1000 nm 

500 nm 


0 nm 

0 nm 500 nm 1000 nm 

29 nm 

0 nm 

FIgurE 8.7 AFM topography image of a collapsed PS-SH brush that was formed in poor 

solvent conditions (concentration: 0.1 mg ml –1 , molecular weight: 144 000 g mol –1 , incubation 

time: 1 h). The imaging has been performed in contact mode under water (bad solvent for PS). 

The polymeric islands can become more extended if the grafting density 

is increased further. This can be attained by using a poorer solvent 

for the polymer solution; under poorer solvent conditions, the size of 

polymer chains is smaller and they can be chemisorbed much closer to 

each other. Figure 8.7 shows an AFM 3D-topography image of PS-SH 

chains end-grafted on the gold substrate from a cyclohexane (poor solvent 

for PS at room temperature) solution. In contrast with the well-separated 

polymer islands formed when the polymer monolayers were prepared in 

good solvent conditions, polymer monolayer formation under poor solvent 

conditions results in elongated and semi-continuous islands upon 

the evaporation of the solvent. 

The lateral inhomogeneity manifested in polymer nanostructures 

and nanopatterns and clearly observed in our experiments is consistent 

with theory and simulations for end-grafted polymer chains at relatively 

high and uniform grafting densities [23–28]. It is to be expected that 

even higher grafting densities will result in a homogeneous layer upon 

the change of solvent conditions or drying of the solvent. However, such 

grafting densities are difficult to attain by a ‘grafting to’ technique like the 

one we employed owing to the steric hindrance of preadsorbed chains. 

Polymer brushes of very high grafting densities can be attained by ‘grafting 

from’ synthetic techniques, where the polymer chains grow from 

low–molecular weight initiators that are immobilized on the surface at 

very high density [17]. 

A polymer brush of uniform density in good solvent conditions forms 

a homogeneous layer that is stretched away from the surface owing to


the repulsive excluded volume interactions between the polymer segments. 

The stretching of the chains is moderated by their entropic elasticity. 

Owing to the thermal agitation and fluctuations, a polymer chain adopts 

an overall shape that allows it to maximise the number of possible conformations. 

Stretching decreases this number, which leads to an entropy 

loss, and for this reason a restoring force of entropic origin develops that 

resists deformation. A polymer brush in good solvent conditions should 

behave like a compliant/soft (non-linear) spring resisting compression, 

protecting the surface and even exhibiting low adhesive and frictional 

forces. An atomic force microscope allows us to probe directly the relevant 

nanomechanical properties at the local level. 

We prepared a polymer brush system by immersing gold substrates to 

a dilute aqueous thiol-terminated poly(methacrylic acid), PMAA-SH, solution 

for 24 h (M w� 66 200 g mol –1 , M w/M n� 2). We used AFM force spectroscopy 

(forward and reverse force distance curves) in deionised water (good 

solvent for PMAA) and acquired many force distance profiles. Two types of 

force profiles were observed on these monolayers. Figure 8.8(a) shows an 

example of the first type. During the forward movement of the tip towards 

the surface (approach), we observe the gradual increasing of the loading 

force owing to the non-linear compressive elasticity of the brush. No adhesive 

force is observed because the brush steric repulsion force screens the 

interaction of the tip with the substrate (in the same way that polymer 

chains anchored on colloidal particles stabilise their suspensions). During 

the reverse movement, there is no adhesion and the polymer brush is 

decompressed in a largely reversible way. Figure 8.8(b) shows that a 

simple exponential does describe the AFM data in the regime of intermediate 

compression of the brush. 

The Alexander–de Gennes theory of a polymer brush [29–31] predicts 

a certain relationship for its compression that can be approximated by 

the following exponential for intermediate compressions (0.2�D/L 0�0.9) 

F (nN) 

(a) 

1.5 

1.0 

0.5 

0.0 

0 20 40 60 

D (nm) 

Forward 

Reverse 

80 100 

F (nN) 

(b) 

10 0 

10 –1 

10 –2 

0 20 40 60 80 100 

D (nm) 

FIgurE 8.8 (a) First type of force profile observed over a polymer brush. Notice the 

absence of hysteresis. (b) Logarithmic plot of the forward force distance curve.


with a spherical probe: F(D) � exp(�2�D/L 0), where F(D) is the force 

exerted on the probe by the brush at a separation D between the probe 

surface and the solid substrate and L 0 is the brush thickness. 

We can directly check this equation on our data. We fitted several force 

profiles with the above equation and we obtained a brush thickness in the 

range of 100 nm, which is of the same order (albeit a bit larger) of the distance 

D, where we observe in force profiles the initial increase of the force, 

signifying the extent (thickness) of the brush away from the surface. The 

discrepancy could arise from the fact that since our probe is small, a large 

proportion of the chains lie near the edge and therefore are expected to 

bend than to compress. A more appropriate theory must take into account 

the spherical shape of the tip and the lateral bending of the chains. 

The second type of force profile is shown in Figure 8.9(a). The force 

profile during probe-tip approach is essentially the same: gradual increase 

of the loading force due to gradual compression of the brush. However, 

during the reverse force profile as the tip moves away from the surface, 

we observe some long-range attractive forces. The full length of one chain 

should be around 120 nm (calculated using the number-average molecular 

weight M n), which is consistent with the stretching events occurring up 

to approximately 200 nm. The magnitude of the attractive forces is in the 

range of 0.1–0.5 nN. Forces in this range can be attributed to physisorption 

of several monomers to a surface. Since we observe a gradual increase in 

the first derivative of these forces, we attribute them on parts of chains, 

individual chains and/or small clusters of chains that were adhered 

non-specifically to the tip and subsequently stretched during the reverse 

movement. The continuous lines in Figure 8.9 correspond to the entropic 

force for a single polymer chain using the freely jointed chain (FJC) model 

with full length approximately equal to the distance between the contact 

F (nN) 

1.5 

1.0 

0.5 

0.0 

Forward 

Reverse 

Theory 

–0.5 

50 

0 50 100 

D (nm) 

150 

(a) (b) 

D (nm) 

80 

70 

60 

Non-linear elasticity 

0.00 0.05 0.10 0.15 

F (nN) 

FIgurE 8.9 (a) Second type of force curve observed over a polymer brush. The continuous 

lines correspond to the theoretical prediction for stretching of individual chains or 

parts of a chain. (b) Zoom of one of the long-range attractive force curves.


point (D � 0) and the minimum of each attractive force. We have assumed 

that the Kuhn statistical segment is b � 0.6 nm. In Figure 8.9(b), we zoom 

on an attractive peak (dashed rectangular in Figure 8.9a). For this plot, the 

variables have been reversed (y � D and x � F) and the absolute value 

of the force has been used. The theoretical formula of the stretching by 

⎡ 

its ends of a freely jointed chain is 

⎛ Fb⎞ 

kT ⎤ 

R � Lc 

⋅ ⎢coth 

⎜ � 

⎝⎜ 

kT ⎠⎟ 

⎥ , where R is 

⎣⎢ 

Fb ⎦⎥ 

the end-to-end chain distance when a restoring force F is exerted, Lc is 

the contour length (full length of the stretched polymer chain), k is the 

Boltzmann constant and T is the absolute temperature [32]. As we can see 

in Figure 8.8, it fits the AFM data well. 

8.4 DIBLoCk CoPoLymErS ADSorBED on SurFACES 

Amphiphilic diblock copolymers have great potential in a variety of 

applications, ranging from their use as responsive layers for the fabrication 

of smart surfaces to supramolecular responsive carriers for drug/ 

gene delivery. We have recently studied the adsorption of poly(isopreneb-ethylene 

oxide) block copolymer (PI-PEO) on mica [33]. The polymer 

consists of a short and very flexible hydrophobic block (PI) (in melt state 

at room temperature) and a long hydrophilic block (PEO). Tapping mode 

AFM imaging was employed in dry state. 

The deposition of a droplet of deionised water polymer solutions 

onto freshly cleaved mica, followed by gentle rinsing and finally 

drying, resulted in the initial formation of ultraflat polymeric islands 

(Figure 8.10a). It is well known that mica is hydrophilic and an adsorbed 

water layer in the form of semi-continuous water islands forms on its 

fresh surface upon cleavage under normal ambient conditions [34, 35]. 

The polymer molecules organised in polymer brush-like flat nanometre-thick 

islands with the PEO within the ultrathin water layer and the 

PI block collapsed at the water/air interface (Figure 8.11a). As mica 

became gradually less hydrophilic with time, most of the water evaporated 

and the polymeric monolayer islands were laterally compressed 

and increased in height (Figure 8.10b). Ultimately, parts of the PEO 

blocks remained adsorbed on to mica (some strongly adsorbed water 

molecules still remain on the mica surface) and other parts aggregated 

owing to the monomer-monomer attractive interactions in the dry state 

and dewetted the mica surface. The dewetting behaviour was aided further 

by the aggregation and fusion of the flexible PI blocks; they came 

together to create a hydrophobic core. The height of the polymer islands 

was increased by a factor of about 5 as mica became less hydrophilic with 

time. The final structure has the organisation of a surface micelle with

1000.0 

950.0 

900.0 

850.0 

800.0 

750.0 

700.0 

650.0 

Y [nm] 

–2300.0 –2200.0 –2100.0 –2000.0 –1900.0 –1800.0 

X [nm] 

8.5 STAR-SHAPEd POLyMERS AdSORBEd ON SURFACES 237 

5.0 

2.0 

0.0 

(a) (b) 

Y [nm] 

(c) 

2600.0 

2500.0 

Z [nm] 

Y [nm] 

600.0 

500.0 

400.0 

a hydrophobic core at the top and a stretched hydrophilic layer partially 

in close contact with the mica surface (Figures 8.10c and 8.11b). 

8.5 StAr-ShAPED PoLymErS ADSorBED on SurFACES 

Star-shaped polymers consist of several linear polymer chains (arms) 

covalently attached to a low–molecular weight core. They are of particular 

interest in soft condensed matter since the number of arms (also called 

functionality) controls their interactions and consequently many physical 

properties. It is expected that as the number of arms increases, their polymer- 

like behaviour will change and become more colloidal-like. 

We adsorbed polybutadiene (PB) star-shaped polymers of three different 

functionalities (number of arms: 18, 32 and 59) onto freshly cleaved 

mica surfaces from dilute polymer solutions in toluene. We investigated 

the structural regimes of the submonolayers and monolayers of adsorbed 

PB star polymers, which were formed on the mica surfaces by using AFM 

tapping mode imaging in dry state [36]. We attained various adsorbed 

300.0 

–2000.0 –1900.0 –1800.0 –1700.0 –1600.0 –1500.0 –1400.0 

X [nm] 

2400.0 

15.0 

12.5 

2300.0 

10.0 

7.5 

2200.0 

5.0 

2.5 

0.0 

–1800.0 –1700.0 –1600.0 –1500.0 –1400.0 –1300.0 –1200.0 

X [nm] 

17.5 

20.0 

Z [nm] 

10.0 

7.5 

5.5 

2.5 

0.0 

FIgurE 8.10 AFM 3D-graph topography of a polymer island (a) 133 min, (b) 745 min 

and (c) 2980 min after sample preparation. 

Z [nm]


Pl 

PEO 

(a) 

(b) 

PEO 

Pl 

FIgurE 8.11 Schematic drawing of the transition over time of the (a) initial brush-like 

flat polymer island to (b) a surface micelle. In (a), the PEO blocks are swollen and stretched 

away due to the presence of a water layer on mica surface and the resulting repulsive 

excluded volume interactions. In (b), most of water has evaporated and parts of the PEO 

blocks remain adsorbed on to the mica surface while other parts come together due to monomer-monomer 

attractions. The PI blocks fuse together in a compact core. 

amounts by employing several incubation times of the mica surface 

within the solution. 

Figure 8.12 shows three examples of topographies of samples prepared 

using relatively short incubation times and consequently low adsorbed 

amounts. In this case, the polymer islands correspond to single and isolated 

polymer chains, as can be deduced by an analysis of their size from 

the AFM images. We can clearly see the asymmetric/irregular shape of 

the low-functionality star polymers and the gradual transition to more 

circular shapes as the functionality increased. Furthermore, the height of 

the individual star polymers increased with functionality; notice the flat 

‘pancake’-like conformation taken by the low-functionality star polymers 

and the increased height of the high-functionality ones. It is clear that the 

higher the functionality, the closer is the star polymer behaviour to the 

one expected for a (soft) colloidal particle; their shape was affected much 

less strongly by the interactions with the surface. 

Figure 8.13 shows an example of an image of sample prepared using 

incubation times in the solution long enough for the 18-arm star polymers 

to start interacting as they were swollen in good solvent conditions. 

Owing to the increased adsorbed amount, i.e. increased number of chains 

adsorbed on the surface, they compressed and confined each other, 

decreasing their lateral extension and simultaneously increasing their 

height. In this way, because of this confinement effect, they became uniformly 

spaced, more symmetrical and circular in shape. At these moderate

Y Range: 1.21 μm 

(a) 

0.205 

–1.00 –0.399 

8.5 STAR-SHAPEd POLyMERS AdSORBEd ON SURFACES 239 

Height range: 2.234 nm 

1.03 1.63 2.24 

X Range: 1.21 μm 


(c) 

–1.71 –1.11 

–2.32 

2 

1.6 

1.2 

0.8 

0.4 


–1.26 –0.652 –0.0473 


adsorbed amounts, no interpenetration and fusion were observed. The star 

polymers continued to keep their individuality and they formed isolated 

globules upon the evaporation of the solvent. 

In Figure 8.14, we compare the overall monolayer organisation for 

long incubation times. Such incubation times are long enough to achieve 

the maximum adsorbed amount (within our adsorption protocol using 

dilute polymer solutions). The 18-arm star polymers organised in discontinuous 

asymmetric islands, which consist of several individual polymer 

chains; it is clear that the star polymers penetrated each other when in 

good solvent and they collapsed in groups upon drying. The 32-arm star 

polymers also penetrated each other and they self-assembled in a continuous 

dense network. On the other hand, the 59-arm star polymers did 


(b) 

–0.56 0.0452 0.65 


–2.59 –1.98 –1.38 


FIgurE 8.12 AFM topography images of star polymers adsorbed on mica: (a) 18 arms, 

incubation time of 5 min; (b) 32 arms, incubation time of 10 min and (c) 59 arms, incubation 

time of 180 min. 

10 

7.5 

5 

2.5 

5 

4 

3 

2 

1



–0.313 

–0.918 

–1.52 


0.634 1.24 1.84 


FIgurE 8.13 AFM topography image of an 18-arm star polymer adsorbed on mica, 

incubation time of 20 min. 

not interpenetrate. The large number of arms and the resulting crowding 

effect and increased osmotic pressure within their volume did not permit 

interpenetration between the star polymers and they continued to collapse 

individually despite the high adsorbed amount. This is a further 

manifestation of colloidal behaviour. 

8.6 ConCLuSIonS 

We have provided several examples of the use of AFM in investigations 

of the fine structure and local nanomechanical properties of polymer 

monolayers and submonolayers. AFM is ideally suited to study the lateral 

inhomogeneities of such ultrathin coatings and their non-linear compliance 

and adhesion either in dry state or within liquid environment. 

Although the time resolution of the (classical) AFM imaging modes (tapping 

mode in particular) is not particularly high, the molecular kinetics 

of polymers on surfaces can be sluggish enough to allow the real-time/ 

real-space monitoring of various physico-chemical surface processes. As 

miniaturisation of electronic and medical devices is rapidly approaching 

the nanometre scale, the AFM is gradually becoming the most important 

characterisation tool of nanostructural and nanomechanical properties. 

Beyond the unique characterisation capabilities, systematic AFM studies 

on model systems can ultimately lead to a formulation of design criteria 

6 

4 

2

Y Range: 1.21 µm 

(a) 

0.403 

–0.201 

–0.806 


–0.67 –0.0649 0.54 

X Range: 1.21 µm 


(c) 

–1.14 –0.536 –0.0684 

–0.461 

ACkNOwLEdgEMENTS 241 

8 

6 

4 

2 


0.144 0.749 


for the processing of surfaces with polymers at the nanoscale for various 

engineering applications. 

ACknowLEDgEmEntS 

The author would like to thank all who have contributed to the 

research reviewed in this chapter, in particular Georges Hadziioannou 

(who also introduced me to this fascinating subject matter), Eric van der 

Vegte, Emmanouil Glynos, Stergios Pispas, Alexandros Chremos, Philip 

Camp, George Petekidis and Jacques Roovers. 


(b) 

–0.976 

–1.59 

–2.20 

Z range: 4.352 nm 

0.341 0.953 1.56 


FIgurE 8.14 AFM topography images of star polymers adsorbed on mica: (a) 18 arms, 

incubation time of 2880 min; (b) 32 arms, incubation time of 2440 min and (c) 59 arms, incubation 

time of 3600 min. 

10 

7.5 

5 

2.5 

4 

3 

2 

1


LISt oF ABBrEvIAtIonS 

AFM atomic force microscope 

FJC freely jointed chain 

PB polybutadiene 

PEO poly(ethylene oxide) 

PI polyisoprene 

PI-PEO poly(isoprene-b-ethylene oxide) 

PMAA poly(methacrylic acid) 

PMAA-SH thiol-terminated poly(methacrylic acid) 

PS polystyrene 

PS-SH thiol-terminated polystyrene 

–SH thiol 

LISt oF SymBoLS 

Unit 

b Kuhn statistical segment M 

D separation distance between the probe surface 

and the solid substrate surface 

M 

F force N 

k Boltzmann’s constant (1.38 � 10�23 ) J K�1 Lc contour length of a polymer chain (full length 

of a stretched polymer chain) 

M 

L0 polymer brush thickness M 

Mn number-average molecular weight g mol –1 

Mw weight-average molecular weight g mol –1 

R end-to-end polymer chain distance M 

T absolute temperature K 

X x-coordinate or abscissa 

Y y-coordinate or ordinate 

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C H A P T E R 

9 

Application of Atomic 

Force Microscopy for 

the Study of Tensile and 

Microrheological Properties 

of Fluids 

Matthew S. Barrow and P. Rhodri Williams 

O U T L I N E 


9.2 Dynamic AFM Methods for the Characterisation of 

Material Properties 249 

9.3 Dynamic Modulation Studies on Confined Fluids 252 

9.4 Determination of Rheological Properties from Resonance Spectra 256 

9.5 Cavitation and Adhesive Failure of Thin Films 259 

9.6 Mesoscale Experimental Studies of the Tensile Behaviour 

of Thin Fluid Films 261 




9.1 InTRoDuCTIon 

Atomic force microscopy is undeniably one of the most successful techniques 

for the characterisation of surfaces and is routinely used to describe 

structural details with nanoscale resolution [1]. The ability of atomic force 

245

246 9. APPLICATION OF ATOMIC FORCE MICROSCOPy 

microscopy to differentiate between local mechanical properties is well 

known, e.g. phase contrast maps obtained using tapping mode [2, 3] may 

be used to identify the distribution of components in composite materials. 

Alternatively, ‘adhesive’ forces may be determined by monitoring the 

deflection of a calibrated cantilever during contact and withdrawal of a 

probe from the surface of a ‘tacky’ material. During this process, the contact 

time and applied force may be varied, and by performing multiple 

tests at different locations, a representative ‘adhesive force map’ may be 

constructed. The atomic force microscope (AFM) is clearly a powerful tool 

for the investigation of forces which govern the mechanics of processes 

occurring at or below the microscale, and the exceptional ability of atomic 

force microscopy to determine forces associated with the microscale deformation 

and flow of fluids is presently discussed. 

An understanding of the rheology of complex fluids is of fundamental 

importance in many practical engineering and biomedical applications. 

Traditional rheometrical techniques, e.g. cone and plate rheometers, require 

reasonably large volumes (i.e. several millilitres) of test fluid, which is often 

undesirable as limited volumes of fluid may be available, e.g. in studies of 

biological fluids. Many processes also involve the deformation of fluids in 

geometric confinement, which are not clearly described by the macroscale 

or bulk rheology alone, e.g. thin film lubrication, and in such instances, it 

is desirable to characterise the fluid mechanics under ostensibly similar 

conditions. Additionally, in such situations in situ measurement of fluid 

rheology is impaired by either the confined space or the extreme process 

environments. 

The rheological behaviour of thin liquid films is an important aspect 

of lubrication [4] and printing [5] – processes which often involve mesoscale 

(0.1�10 �m) thickness films undergoing rapid deformation between 

separating surfaces. In the case of fluid mechanical machinery, they are 

usually solid surfaces whereas in biomechanics they may be flexible 

surfaces such as biological membranes. The ‘cracking’ of knuckle joints has 

been attributed to cavitation within mesoscale lubricating films of synovial 

fluid [6] whereas surface damage in microelectromechanical systems 

devices has been attributed to the cavitation of lubricant films [7]. The 

ability of liquids to sustain tension is an important factor in the survival 

of plants in which the cohesion–tension (C–T) theory has been proposed 

to explain water transport [8]. The C–T theory assumes that water, when 

confined in small tubes with wettable walls such as xylem elements, can 

sustain a tension ranging from 3 to 30 MPa. The liquid forms a continuous 

system in the water-saturated cell walls from the evaporating surfaces of 

the leaves to the absorbing surfaces of the roots. During evaporation, the 

reduction in water potential at the surfaces causes movement of water out 

of the xylem, with water loss producing tension in the xylem sap that is 

transmitted throughout the continuous water columns to the roots.

9.1 INTROdUCTION 247 

In coating processes, cavitational film splitting may result in the formation 

of rapidly stretching filaments, whose breakup leads to unwanted 

droplet deposition. Filament formation is also a feature of coating flows 

involving adhesive films [9], but descriptions of the process are still 

largely qualitative, invoking terms such as ‘tack’ [10, 11]. The tack of an 

ink film is primarily connected with the tensile forces developed in film 

splitting [12], the function of cavitation being to limit the forces of separation 

of surfaces joined by a tacky liquid [13]. By definition, the tack of 

an ink film is the maximum tensile stress (or ‘negative pressure’) which 

can be withstood by it before splitting [5]. 

The subject area of micro- and nanorheology [14–18] has developed 

rapidly and benefited from the advent of the AFM and the surface force 

apparatus (SFA) [19, 20]. Roughly speaking, there are two principle objectives 

driving the development of AFM-based rheometrical techniques, the 

first considers the ability of AFM to describe the microrheological properties 

of thin fluid films [21] whereas the second seeks to exploit AFM 

microcantilever technology as the basis for microsensor devices [22], 

which, e.g. may be incorporated into the so-called lab on a chip device. 

Specifically, it is envisaged that the development of MEMS devices such 

as diagnostic sensors incorporating microfluidic components can greatly 

benefit from an improved understanding of the microscale rheology. 

In this respect, the determination of viscosity and density (or even simple 

representative damping coefficients) inferred via microflexural responses is 

of fundamental interest. This is because microcantilevers present a viable 

means by which the rheological properties of microvolumes of fluids may be 

assessed in situ. As an example, the resistive forces arising due to the motion 

of a cantilever within a minute volume of liquid can be analysed through 

changes in the cantilever response, as an immersed cantilever undergoing 

stimulated oscillation will experience fluid damping effects which are interrogable 

via resonance characteristics [23, 24]. Similarly, the ability to detect 

adsorbed mass (by monitoring changes in the resonance characteristics) in 

conjunction with functionalisation of the cantilever (or probe) surface represents 

a potential approach to biomolecule or chemical species detection [25]. 

As the forces accompanying indentation or compression of a material 

by an AFM probe may be resolved with extreme accuracy, AFM-based 

techniques are particularly suited to rheological studies of predominantly 

elastic materials [26, 27]. In the simplest case, cantilever deflection may 

be used to describe the compliance of the surface in a simple qualitative 

manner, e.g. for a rigid, essentially undeformable material, the deflection 

of the cantilever will be equivalent to the downwards displacement of the 

piezoceramic actuator whereas for softer materials the probe will compress 

and indent the sample such that the cantilever deflection is lower. 

Probe–surface interactions assuming ideal elastic interactions are often 

used to determine the Young’s modulus of the material via derivatives of


the Hertz model (i.e. sphere against sphere compression) for non-adhesive 

systems. Furthermore, the Hertz model is readily adapted to provide 

idealised descriptions of geometries such as conical tips compressing flat 

substrates [28]. 

Notwithstanding the fact that AFM is routinely used in studies where 

elastic deformations are satisfactorily described by idealised models – a 

limitation of the use of AFM in many rheological experiments, particularly 

those involving fluids, is the assumed description of both the geometry 

and the flow field contained within. 

Therefore, for the AFM-based study of fluids, the use of colloid probes 

[29] has proved to be of considerable benefit. Colloid probes (which are 

fabricated by attaching a colloid sphere to the underside of an AFM cantilever) 

have found favour in several different research areas including the 

drainage of thin films [30], interfacial forces [31], mechanical properties 

of cells [32–34], lubrication theory [35] and the deformation of colloidal 

droplets [36, 37] to name but a few. 

As has been alluded to previously, the successful use of AFM in 

microrheological and tribological studies is facilitated by the ability to 

describe force through the deflection and known spring constant of the 

cantilever. However, the topographical imaging capability of an AFM has 

been used as a component part of some studies. The imaging capabilities 

of an AFM have been used to measure the biaxial extensional deformation 

involved in the industrially important process of bubble inflation [38]. 

In this method the force-measuring capabilities of the AFM are not fully 

exploited, instead the AFM is used to measure the radius of curvature of 

microbubbles produced by inflating a thin polymer film, which is adhered 

to a porous silicon substrate. A similar approach is used to study the surface 

properties of polymers by using an AFM to measure the embedding 

rate of nanoparticles at temperatures near to the glass transition temperature 

of the polymer [39]. 

Considering force measurement, one technique of particular relevance 

to tribology and lubrication studies is lateral force measurements in friction 

force microscopy (FFM) [40–44], which considers the torsion of a cantilever 

arising from frictional forces generated between a scanning tip and a surface. 

As lateral perturbations are caused by both frictional forces and surface 

features, it is informative to consider the local surface topography. The influence 

of surface features upon the lateral deflection becomes apparent if the 

surface is scanned in opposing directions, as a topography-induced torsional 

response is dependent upon the scan direction (the torsion is reversed) 

whereas the lateral deflection arising from the effect of the frictional component 

will remain unchanged (Figure 9.1). 

The beneficial application of microrheometry as an adjunct to traditional 

bulk rheometry is demonstrated by the application of AFM force 

studies (including dynamic FFM, [45]) to adhesive materials. For example,

Cantilever 

Scan direction 

9.2 dyNAMIC AFM METHOdS 249 

Friction force 

FIguRE 9.1 FFM monitors the lateral deflection, i.e. tilt or ‘twist’ of the cantilever due 

to frictional resistance or drag forces in thin fluid layers acting upon the scanning tip. 

a combination of lateral force microscopy and indentation has been used 

to investigate the surface properties of pressure-sensitive adhesives (PSAs) 

[46], where the tack of the adhesive in response to various compressive 

loads is of paramount importance. Differences in local frictional forces due 

to increased adhesive force between the tip and the PSA arising from the 

incorporation of tack promoting components (tackifiers) may be identified. 

Therefore, FFM may be used to first identify microscale regions of varying 

surface friction, following which the AFM can determine ‘adhesive’ 

characteristics of the different tackifier enriched or depleted regions. The 

correlation between traditional bulk tack and adhesion force as measured 

by AFM (or nanotack) is also considered by other workers [47], who find 

that the AFM force data are in general agreement with bulk tack tests. 

9.2 DynAMIC AFM METhoDS FoR ThE 

ChARACTERISATIon oF MATERIAL PRoPERTIES 

The nanorheological properties of polymeric liquids can be obtained 

by adapting techniques such as an SFA or an AFM to act in a dynamic 

mode [48, 49]. However, the results of AFM studies are often more 

difficult to interpret than those derived from SFA experiments due to 

uncertainties about the zero separation distance, the influence of probe 

asperities and torsional deflections. 

Dynamic AFM, especially force modulation microscopy (FMM) [50–55], 

as a technique to determine the dominant elastic (and also viscoelastic) 

properties of materials has been investigated in many studies including 

the drainage of confined fluid layers [56], elastohydrodynamic lubrication 

studies [57], approximations to the viscoelastic moduli of solvated 

polymer layers and the evaluation of temperature-induced variations in 

micromechanical properties [58]. Force modulation studies involve applying 

a small amplitude (typically a few nanometres), sinusoidal oscillation 

Tilt


to either the probe or the sample substrate and observing the amplitude 

and phase response of the cantilever when the probe is either in contact 

with the surface of the material or is in close proximity to a surface 

with an intervening fluid layer. Although many forms of the modulation 

technique have been employed to characterise predominantly elastic 

materials, comparatively few AFM studies use superimposed modulation 

to study confined liquids. 

Various terms are used to describe dynamic modes of operation 

although many of the reported modes are essentially similar in design. 

Tapping mode (or intermittent contact) imaging is perhaps the most familiar 

dynamic AFM technique. In tapping mode the cantilever is oscillated 

at or near its resonance frequency such that when the tip interacts with the 

sample surface, the amplitude and phase response will change. In response 

to this deviation, a feedback loop adjusts the height of cantilever above the 

surface to achieve a constant vibration amplitude. Phase contrast images 

obtained from tapping mode studies are routinely discussed in terms of 

the perceived damping effects induced by the elasticity or compliance of 

the sample surface. Most commonly, qualitative interpretation of the phase 

data may be used to discern areas of varying stiffness. FMM is essentially 

a dynamic mode of operation in which the tip and substrate interact under 

conditions of a constant (average) force such that the amplitude of the 

cantilever oscillation varies about a nominal set point. Modulated force 

experiments are often performed at a single point upon the surface, and 

for the case of intervening liquids, the amplitude and phase are often monitored 

as a function of probe to surface distance. 

Considering predominantly elastic surfaces, FMM is often used to 

generate surface images, which are generally referred to as either ‘elasticity 

maps’ or ‘viscoelasticity maps’, depending upon the interpretation 

of the force data. The fundamental approach employs single-point force 

modulation [59] in which an ‘AC modulation’ is superimposed upon 

either the probe or the sample during a ‘DC’ (i.e. force–distance) experiment. 

If the modulation frequency is sufficiently high, the technique may 

be employed while scanning a surface and is a complementary approach 

to point-wise force mapping [28]. 

The basic method and interpretation is considered by Maivald et al. 

(1991) [52] who exploit variations in local surface elasticity to provide a 

basis for image contrast in inhomogeneous materials. The probe is scanned 

across the surface with the feedback loop maintaining contact with a 

(nominal) constant cantilever deflection and therefore a constant applied 

force. If the sample is caused to oscillate a small distance �z 1 in the direction 

normal to the surface, the undulating motion of the surface produces 

a corresponding superimposed deflection of the cantilever �z 2. For an 

infinitely hard sample, the deflection of the cantilever will be such that 

�z 1 � �z 2, whereas in the case of softer samples the sample surface will

9.2 dyNAMIC AFM METHOdS 251 

be compressed by a distance �z 3 such that �z 1 � �z 2 � �z 3. Therefore 

the deflection of the cantilever �z 2 is less on softer materials, and the term 

�z 2/�z 1 is deemed to be indicative of surface compliance (Figure 9.2). 

This method can be implemented using the advanced capabilities 

of modern AFMs, one approach is similar to that described by Scott and 

Bushan (2003) [2]. In this example, the modulating amplitude is obtained 

by inducing vibration of the cantilever, the sample remaining fixed in position. 

Using an interleaved scanning approach, the sample height is first 

determined using tapping mode. The probe height is then adjusted such 

that (i) the probe is kept in constant contact with the surface and (ii) a constant 

scan height is maintained by compensating for the known sample 

height variation, i.e. the distance between the fixed end of the cantilever 

and the surface is held constant. The surface is then rescanned with the 

oscillating probe driven, in this case, at the resonant frequency (Figure 9.3). 

Clearly, the method by which the sample–tip interaction is spatially 

modulated can be achieved in several ways. The probe may be caused 

1 

1 2 

FIguRE 9.2 FMM: discrimination between areas of varying stiffness. (1) Hard substrate 

and (2) soft substrate; cantilever deflection signal �z 2 is reduced due to deformation of the 

sample. 

2


Surface profile from primary scan 

FIguRE 9.3 Interleaved scanning wherein the force modulation scan uses the predetermined 

sample height. 

to oscillate by (i) the influence of an external driving force (such as a 

magnetic field), (ii) vibrating the sample using an electromechanical 

oscillator, (iii) mounting the cantilever on a secondary piezoceramic oscillator 

or (iv) modifying the primary piezoceramic scanner voltage. The 

preferred method may be influenced by the apparatus and the desired 

frequency range, as some oscillators exhibit mechanical resonances and 

produce excessive acoustic interference, the latter problem is likely to be 

more pronounced when the sample is contained in a small liquid cell. 

A wide range of modulation frequencies and experimental methods have 

been employed, ranging from a few hertz to several megahertz, and 

although the basic excitation principle is retained, the analytical methods 

vary significantly. For example, atomic force acoustic microscopy 

(AFAM) employs excitation frequencies to several megahertz in order to 

elicit sample-specific, frequency-dependent spectra derived from contact 

measurements [60, 61]. 

9.3 DynAMIC MoDuLATIon STuDIES on 

ConFInED FLuIDS 

For those studies where the viscoelastic response is of interest, 

attempts are made to relate the deflection amplitude and phase of the 

cantilever to the dynamic complex modulus G*(�) of the material. In 

standard rheometry, a sample subjected to a sinusoidally varying shear 

stress will respond with a sinusoidally varying shear strain, and the 

mechanical characteristics of the sample may then be described by the 

complex modulus as given by 

�( �) 

G*( �) 

� 

ε( �) 

(9.1)

where � is the shear stress, ε the shear strain and � the frequency. The 

complex modulus may be described as the summation of an in-phase 

elastic component and an out-of-phase viscous component, i.e. 

G*( �) � G′ ( �) � i G′′ 

( �) 

(9.2) 

and 

9.3 dyNAMIC MOdULATION STUdIES ON CONFINEd FLUIdS 253 

G′ 

( �) 

� tan � 

G′′ 

( �) 

(9.3) 

where G� is the storage (elastic) modulus, G�″ the loss (viscous) modulus 

and � the phase angle between stress and strain. 

The analogy between bulk oscillatory and dynamic scanning probe 

microscope techniques is discussed by Suraya et al. (2008) [62], where 

for the latter, the motion of one surface imparts oscillatory motion to 

the fluid due to hydrodynamic forces, which in turn invokes oscillation of 

the ‘receiver’ surface, i.e. the colloid probe. However, although the receiver 

surface will oscillate at the same frequency, viscous effects are such that the 

oscillation amplitude is attenuated and the phase is shifted (relative to the 

driven surface). For an inelastic liquid, the detected signal will be 90° outof-phase, 

whereas an elastic response is expected to be in-phase with the 

driven surface. When oscillating surfaces bearing adsorbed polymer layers 

are immersed in dilute polymer solutions, the vibrating motion produces 

a viscous response at large surface separations. As the separation distance 

is reduced, the polymer layers interact and deform, and the viscoelastic 

properties of the material become apparent as the receiver amplitude 

increases and the phase shift reduces. 

Suraya et al. (2008) note that the measurement of the effect of the hydrodynamic 

force upon the phase and amplitude is insufficient to directly 

measure the stress and strain in the fluid layer. To translate the measured 

parameters into terms which are physically representative of the stress 

and strain, a mechanical model is required. A common approach employs 

hydrodynamic lubrication equations, which conveniently describe the 

hydrodynamic force that arises from the flow of a purely viscous liquid 

between a flat surface and a colloid sphere, the force F is given by 

F U R 

� 6 π η , ( h


The application of hydrodynamic lubrication approximations (equation 

(9.4)) is illustrated by the viscous damping coefficient described in 

the work of Friedenberg and Mate (1996) [63] who studied the amplitude 

and phase response of a colloid probe in contact with a thin film of lowmolecular-weight 

poly(dimethylsiloxane) (PDMS). The PDMS film was 

constrained between a sphere attached to a tungsten cantilever and a flat 

substrate – the substrate being subjected to oscillatory motion. Both the 

separation distance between the sphere and the surface h and the vibration 

frequency � were varied (Figure 9.4). 

A simple viscous model incorporating the contribution of meniscus 

forces is considered, which relates both amplitude and phase to a single, 

viscous damping coefficient b p. Equations (9.5) and (9.6) show the simplest 

form of the derived model when capillary forces are neglected. 

� φ 

� � bp 

k 

sin 

tanφ 

b 

p 

� 

� 

k 

bp 2 

6π�R 

� 

h 

(9.5) 

(9.6) 

(9.7) 

where � is the ratio of cantilever and drive amplitudes, k and φ the spring 

constant and the phase difference between the substrate and cantilever 

motion and R the radius of the sphere. 

PDMS fluid 

Silicon 

substrate 

Tungsten 

cantilever tip 

FIguRE 9.4 Schematic diagram of the probe–fluid geometry (Friedenberg and Mate, 

1996, the illustrated geometry has been rotated 90°). As the probe is not fully immersed, 

capillary forces affect the contact area. 

h 

dz

The value of the viscous damping coefficient b p is then determined by 

fitting the measured values of both amplitude and phase as a function of 

separation distance h to equations (9.5) and (9.6). The apparent viscosity 

of the fluid � may then be calculated from the damping coefficient and 

equation (9.7). Using this method reasonable agreement between the calculated 

viscosity and measured ‘bulk’ viscosity was found; however, the 

results also indicated that the surface roughness of the sphere may cause 

deviations from the expected zero-intercept relationship inferred from 

equation (9.7) (i.e. 1/b p vs. h). Choi and Kato (2003) [64] have extended 

this approach to investigate the shear properties of perfluoropolyether 

liquid bridges formed between two glass spheres by inducing lateral oscillations 

(as opposed to the normal perturbations depicted in Figure 9.4). 

Suraya et al. (2008) [62] have reported the use of dynamic AFM to 

investigate the viscoelastic response of adsorbed hydroxypropyl guar 

(HPG) layers. The results identified dominant viscous properties at large 

surface separations and viscoelastic behaviour at closer separations 

where the polymer layers interact. The adsorbed polymer also exhibited 

viscoelastic frequency dependence and ‘shear thinning’ characteristics. 

Similar studies were performed by Braithwaite and Luckham (1999) 

[65] who studied the viscoelastic response of adsorbed layers of gelatine 

under compression using dynamic modulation. The system consisted 

of a colloid probe interacting with a hard substrate where both surfaces 

were coated with a thin film of adsorbed gelatine. The model employed 

considers the characteristics of the viscoelastic materials as discussed by 

Radmacher et al. (1993) [66]. 

In such studies, as the actual values of stress and strain in the sample 

cannot be determined directly, they are instead speculatively related to 

the force F and displacement z of the cantilever through the use of an 

‘apparatus coefficient’ b such that for a given frequency: 

� 

ε 

� � G 

1 F 

* 

b z 

(9.8) 

From which an alternative definition of the storage and loss moduli may 

be described [65, 66] wherein the equations are of the form: 


9.3 dyNAMIC MOdULATION STUdIES ON CONFINEd FLUIdS 255 

�k (cos φ � �) 

G′ 

( �) 

� 

2 b � � 2 � cosφ 

� 1 

�k sin φ 

G′′ 

( �) 

� 

2 b � � 2 � cosφ 

� 1 

(9.9) 

(9.10)


where k is the cantilever force constant, � the ratio of cantilever to substrate 

modulation amplitude and φ the phase angle between substrate 

and cantilever response. It is important to note that the equivalence of 

the phase terms φ and � is not always physically representative, and a 

quantitative description of the rheological properties of a homogeneous 

fluid sample may be verified under some conditions; however, when the 

sample fluid is non-uniform, e.g. an adsorbed polymer layer is present, 

only qualitative information can be obtained. 

9.4 DETERMInATIon oF RhEoLogICAL PRoPERTIES 

FRoM RESonAnCE SPECTRA 

The resonance characteristics of microcantilevers immersed in fluids 

have long been recognised as a potential basis for rheometrical microsensor 

technology as the resonance spectra of a vibrating cantilever are 

influenced by the viscosity and density of the surrounding medium. 

Compared to vibration in air, the fundamental resonant frequency of a 

rectangular cantilever is reduced when operated in liquid; immersion 

in increasingly more viscous liquids reduces the resonant frequency 

further – this is accompanied by a broadening of the resonant peak and a 

decrease in peak amplitude (Figure 9.5). 

The shift in the mechanical response is attributed to the viscous 

drag and inertial effects caused by the fluid adjacent to the cantilever. The 

resonance characteristics are often derived from the effect of environmental 

stimuli – most commonly thermally induced vibrations. The thermal 

noise spectrum is derived from the Fourier transform of the displacement 

of the cantilever. Fast Fourier transforms (FFTs) are routinely used 

in sound and vibration analysis to convert a signal from a time domain to 

A 

High viscosity 

ω 

Low viscosity 

FIguRE 9.5 Resonance frequency shift due to immersion in viscous fluids.

a frequency domain such that the relative magnitude of each frequency 

component may be evaluated and the resonance spectrum constructed. 

The motion of the cantilever may be modelled as a simple harmonic 

oscillator (SHO) with an increased effective mass due to the contribution 

of the fluid in close proximity to the beam. Simple approximations 

describing the contribution of the fluid mass are described by Oden et al. 

(1996) [83], who model the virtual mass of the SHO as the combination 

of the cantilever mass and the mass of a spherical fluid volume enveloping 

the cantilever. More advanced models are considered by Sader (1998) 

[67], who present analytical expressions for the hydrodynamic functions, 

which determine the hydrodynamic loading due to the motion of the 

mass of fluid around a rectangular beam. The theory considers cantilevers 

with rectangular and cylindrical cross-sections for which the length 

is far greater than the diameter or width, respectively. 

For beams of a circular cross-section, the analytical expression for the 

hydrodynamic function � has been established previously; however, rectangular 

beams of finite thickness are far more complicated to describe. 

Sader (1998) derives a correction factor �(�) which relates the circular 

cross-section solution to that of an infinitely thin rectangular cantilever 

based on the approximate relationship previously described by Tuck 

(1969) [69] such that the hydrodynamic function � rect is given by: 

� ( �) � �( �) � ( �) 

rect circ 

where the correction factor �(�) is of the form 


9.4 dETERMINATION OF RHEOLOgICAL PROPERTIES FROM RESONANCE SPECTRA 257 

�( �) � � ( �) � i� 

( �) 

r i 

� ( �), � ( �) � (Re) 

r i f 

(9.11) 

(9.12) 

(9.13) 

For small amplitude oscillations, the characteristic Reynolds number 

depends upon the cantilever width x such that: 

� � 

Re � 

4� 

fluid x2 

For an SHO the amplitude A(�) is given by 

A0�R 

A( 

�) 

≅ 

⎡ 

⎢ 2 2 � � 

⎢( 

� �R) 

⎣ 

Q 

2 

� � 2 

2 

1 

2 2 2 

R 

⎤ 

⎥ 

⎦ 

(9.14) 

(9.15)


where A 0 is the zero-frequency amplitude response, � and � R are the 

radial and radial resonant frequencies, respectively [70], 


� 

R 

� 

� 

⎡ 

⎢ 

π�x 

⎢ 

1 � 

⎣ 4� 

vacuum 

2 

⎤ 

� r( �R) 

⎥ 

⎦ 

4� � �r( 

� 

2 R) 

π�x 

Q � 

� ( � ) 

i R 

1 2 

(9.16) 

(9.17) 

where � (�� cxt) is the mass per unit length of the cantilever of density � c, 

width x and thickness t. � r and � i are the real and imaginary parts of the 

aforementioned hydrodynamic function �(�). 

For an unknown fluid, the fundamental resonance profile is used to 

determine � R and Q from equation (9.15). The method is not restricted to 

the use of the fundamental resonance mode, and higher resonance peaks 

may be used although the accuracy of the result is reduced. Provided 

� vacuum is known, the experimentally determined values of the resonance 

frequency and the quality factor may then be used to determine the viscosity 

and density by numerically solving equations (9.16) and (9.17). 

The SHO model is useful for the determination of both viscosity and 

density provided Q � 1. If the cantilever response is heavily damped, 

Q � 1, then the SHO model is not valid. However, this may in some 

instances be circumvented by the selection of a cantilever with different 

mechanical properties. 

Maali et al. (2005) [71] have evaluated a simplified approximation for 

the hydrodynamic function �(�) and propose that 


�r( �) 

� a � a 

1 2 

� 

� 

� ⎛� 

⎞ 

�i( �) 

� a3 � a ⎜ 4 

� ⎝⎜ 

�⎠⎟ 

2 

(9.18) 

(9.19) 

where a 1, a 2, a 3 and a 4 are constants and � is the characteristic thickness of 

fluid surrounding the cantilever equivalent to an exponential damping 

length �, where 

� � 

2� 

� � 

fluid

9.5 CAvITATION ANd AdHESIvE FAILURE OF THIN FILMS 259 

The accuracy of the model proposed by Sader (1998) was evaluated 

using several fluids including air, water, acetone, carbontetrachloride 

and butanol, which presented wide viscosity and density ranges. Results 

were presented for both precision fabricated and standard cantilevers, 

and in both cases the theoretical and experimental results for the Q factor 

and resonant frequency as determined from the thermal resonance 

spectra were in close agreement [72] as were the viscosity and density 

results [70], which were found to be in accordance with known bulk 

measurements. 

The resonance methods described provide a basis for the in situ determination 

of both viscosity and density of inelastic liquids. However, the 

use of resonance data to elucidate viscoelastic parameters is extremely 

complicated. In this respect, the use of a modified Langevin model which 

incorporates a complex drag coefficient in an attempt to overcome the 

limitations of the simplified SHO model has also been studied [73–75]. 

9.5 CAvITATIon AnD ADhESIvE FAILuRE 

oF ThIn FILMS 

Due to the high deformation rates which typify many mesoscale phenomena, 

such as film splitting, filamentation and cavitation processes, 

significant viscoelastic effects may be anticipated. One such effect is a 

delay in the cavitation of viscoelastic liquids in micrometre-sized gaps, 

due to the development of normal stresses [76]. Others claimed that 

viscoelastic effects include a displacement of the point of cavitation from 

the centre of contact (where film thickness is a minimum) and enhanced 

film thicknesses [77]. Little is known about the influence of viscoelasticity 

in sub-micron liquid film cavitation, but the initial film thickness is a 

crucial factor: for sufficiently thin films, even ostensibly low rates of 

surface separation may provoke the high rates of fluid deformation necessary 

to generate enough tension (through viscous forces) to result in 

cavitation [78]. 

It is important to realise that in ultrathin films of water, cavitation may 

occur spontaneously, due to the antipathy between the liquid and hydrophobic 

surfaces between which it is confined [79]. Spontaneous cavitation 

was first observed experimentally by Christenson and Claesson (1988) 

[79]. Theory predicts that vaporous cavities will only form in pure liquids 

as a result of large tensions, some 1300–1400 bar in the case of water [80], 

although a somewhat higher figure (ca. 1900 bar) results from an interpretation 

of the thermodynamic properties of stretched water known 

as the stability limit conjecture [81]. Experiments involving very small 

quantities of pure water have produced tensions close to this homogeneous 

nucleation limit [82], but they are not commonly observed.


Berard et al. (1993) [83] showed that the free energy of a bridging cavity 

is lower than that of liquid water when the surfaces are separated as far as 

micrometres and claim that the fact that such cavities are not observed as 

the two surfaces approach contact from far apart indicates that the liquid 

between them is metastable, i.e. there is some barrier preventing cavitation. 

The theory for the long-ranged hydrophobic attraction relies upon 

this notion of induced cavitation – the force between two colloids in a 

near-critical or a near-spinodal fluid is attractive and long-ranged – and 

the connection between the spinodal attractions in the bulk and measured 

long-range attractions between hydrophobic surfaces is the observed 

cavitation [84]. 

Computer simulations by Berard et al. [83] on a Lennard–Jones liquid 

confined between hard walls showed cavitation at small separations, and 

that there was indeed a spinodal separation. Approaching this separation 

it was found that the attractions were much stronger than the van der 

Waals attraction and longer ranged. Qualitatively, a separation-induced 

spinodal can account for the measured hydrophobic attractions. 

In the case of cavitation which results from the development of fluid 

mechanical stresses (as tension), Joseph [78] has pointed out that the concept 

of ‘negative pressure’ is not particularly useful; it is more pertinent to 

consider the state of stress experienced by a liquid. In doing so, it is convenient 

to decompose the stress into a deviator and mean normal stress, 

the most positive value of principal stresses being the maximum tension. 

In order to facilitate a comparison of a liquid’s cavitation threshold stress 

with the principal stresses at each point within the liquid, it is necessary 

to know the flow field. In terms of studying cavitation inception within 

mesoscale liquid films, this requirement imposes stringent experimental 

demands as it requires a comparison of the cavitation threshold at each 

point in a liquid sample with the principal stresses there. For liquids in 

motion, cavitation criteria must be based not on the pressure, but on the 

stress, and a cavitation bubble will open in the direction of maximum tension 

in principal coordinates. An important point which emerges is that 

a liquid can cavitate as a result of experiencing a shear deformation, the 

resulting cavity being pulled open by tension in the direction defined by 

principal stresses. 

Of the few experimental techniques capable of working at (or below) 

the mesoscale, the various ‘force microscopes’, such as the SFA, have been 

the most successful, but instances of their use in studies of thin fluid films 

are comparatively rare. Notable exceptions are provided by the work of 

Israelachvili and co-workers [85] who observed the growth and disappearance 

of vapour cavities in liquid films between separating mica surfaces in 

SFA experiments. The growth of a cavity was claimed to represent a ‘new’ 

cavitation damage mechanism, insofar as surface damage occurred during 

cavity inception [86]. This is an interesting finding given that by far

9.6 MESOSCALE ExPERIMENTAL STUdIES 261 

the greatest effort in cavitation damage research has involved the study of 

bubble collapse and its consequences. Lord Rayleigh’s seminal analysis of 

the collapse of an isolated spherical void in an incompressible liquid [87] 

leads to the conclusion that, as the collapse nears completion, the pressure 

inside the liquid becomes indefinitely large. It is principally this ‘Rayleigh 

collapse’ mechanism (albeit extensively modified) which has led to the 

association of bubble collapse with cavitation damage [88]. 

Little is known about the dynamics of cavities formed in thin films but, 

due to their inevitably close proximity to the film’s bounding surfaces, significant 

departures from spherical symmetry may be anticipated [89]. The 

asymmetry of cavity collapse leads to potentially damaging phenomena, 

such as liquid jets [90], but the issue of cavitation damage due to cavity 

growth has received relatively little attention, despite the possibly damaging 

consequences to capillaries and small blood vessels due to the intraluminal 

expansion of cavitation bubbles in the areas of laser angioplasty [91], 

electrohydraulic lithotripsy [92] and shock wave lithotripsy [93]. 

9.6 MESoSCALE ExPERIMEnTAL STuDIES oF 

ThE TEnSILE BEhAvIouR oF ThIn FLuID FILMS 

As discussed, many processes of emerging scientific and technological 

interest involve the rheological behaviour of complex fluids in the mesoscale 

domain (ca. 0.1–10 �m), and in order to study the mesoscopic behaviour of 

fluids, particularly filament formation (i.e. extensional flow) and cavitationinduced 

failure and tack, it is necessary to satisfy some basic requirements. 

Notwithstanding the fact that the creation of a liquid bridge between a colloid 

probe and a flat surface is a fairly straightforward process, manipulation 

of the desired quantity of fluid is not. Therefore in addition to recording 

the evolution of tensile forces, the deformation of the fluid should ideally be 

recorded. Although instruments such as the AFM suggest themselves for 

adaptation in terms of the former requirement, the latter task (i.e. recording 

the deformation of mesoscale filaments with sufficient temporal resolution) 

is non-trivial. But it is one which must be accomplished as a precursor to the 

development of a satisfactory mesoscale extensional flow technique. 

Extensional flows of complex fluids may be studied using several macroscale 

techniques such as the filament stretching rheometer (FSR) or the 

capillary break-up extensional rheometer (CaBER), whose illustrations are 

shown in Figures 9.6 and 9.7. In these techniques the characteristic dimensions 

and the quantity of liquid are known, whereas the interpretation of 

results from AFM-based microrheometry is restricted by the necessary 

assumptions about the flow field. 

As a colloid probe moves rapidly away from a surface, it is reasonable 

to assume that the fluid confined between the surface and the sphere may


FIguRE 9.6 Formation of macroscopic viscoelastic liquid filaments formed in a filament 

stretching rheometer. The fluid is constrained between the ends of two cylinders, which are 

pulled apart at a specified rate. The generated tensile force and the filament profile are used 

to calculate the extensional stress. The cylinder shown is 10 mm in diameter. 

FIguRE 9.7 Images showing a typical CaBER experiment on a biopolymer solution. 

The surfaces are separated at a predetermined distance, thereafter the temporal evolution of 

the surface profile is used to determine rheological properties. Cylinder diameter is 2 mm. 

be extended. If the initial minimum separation distance is sub-micron 

and the retraction event is sufficiently rapid, then the stresses generated 

within the liquid may approach or exceed the tensile strength of the liquid. 

However, in AFM studies the fluid is not directly observed, therefore 

fluid draining, viscoelastic filamentatious behaviour or cavitational failure 

is not readily substantiated. It is, therefore, useful to examine those 

means by which the deforming liquid can be observed and documented. 

The separation distances considered in most AFM force studies are near 

to, or beyond, the limits of conventional optical microscopy. Although it 

is not possible to observe nanofilaments through an optical microscope,


FIguRE 9.8 Photograph of unmodified (left) and modified (right) explorer AFMs. 

The base-section of the modified AFM has been modified to provide access for peripheral 

lenses. 

the observation of microfilaments is plausible. For cavitation and tackrelated 

phenomena, the rates of separation may be comparatively high, 

and in order to verify the existence of microfilaments and determine 

their form by direct visualisation, high-speed video microscopy studies 

are necessary. 

The combination of high-magnification microscopy and high-speed 

video presents a considerable challenge due to the illumination requirements, 

particularly when using high magnifications, optical filters (often 

necessary due to diffuse reflection of the AFM laser source) and fast 

shutter speeds. The design of most AFMs restricts direct observation of 

confined fluid samples, as the physical dimensions do not readily permit 

the inclusion of supplementary (high-speed) imaging systems. Several 

different AFMs have been used to study microfluidic aspects including 

a Thermomicroscopes Explorer, a Digital Instruments Dimension 3100, 

a Veeco Multimode and more recently a PSIA XE-120 with optical head. 

Studies using high-speed video systems, namely, a Kodak Ektapro 4540 mx 

and a Photron APX Fastcam, were used to record microfluidic defomation 

using ‘cold light’ sources to reduce the effect of evaporation when studying 

microlitres of aqueous polymer solutions. 

The enclosed nature of the Explorer prevents the use of peripheral 

lenses; therefore a section of the base of the AFM was removed (shown 

in Figure 9.8). For the Dimension 3100, the colloidal probe and cantilever 

are unobtrusively located beneath the scanner such that an objective lens


may be positioned adjacent to the cantilever holder. For the multimode 

system, a light intensified high-speed camera (an APX I2 intensified 

head) was employed due to illumination restrictions. Photomicrographic 

studies using the XE-120 (optical head system) are readily achieved as 

the optical head system permits peripheral access. 

The selection of a suitable microscope assembly is determined principally 

by the minimum attainable distance between lens and colloid 

probe; therefore ultralong working distance (ULWD) lenses were used 

(with supplementary lenses) as shown in Figure 9.9. 

Separation of the surfaces is achieved either by raising the probe (conventional 

force–distance) or by lowering the sample substrate using a 

piezoceramic actuator. The Explorer is especially suited to the latter as it 

may be positioned above an independent piezoceramic stack. 

Figure 9.10 shows filamentatious behaviour of a viscoelastic polymer 

(the V-shaped cantilever is 85 µm long). The fluid is stretched between 

FIguRE 9.9 The high-speed optical microscopy system incorporating (1) APX Fastcam 

high-speed camera, (2) extension tube, (3) supplementary macrolens magnification and 

motorised focus, (4) light source and (5) ULWD microscope lens. 

FIguRE 9.10 Formation of microscale viscoelastic liquid filament formed between a 

V-shaped cantilever and a reflective silica substrate.


a ‘bare’ cantilever and a reflective silica substrate, the reflected image is 

apparent in the lower half of the figure. When probeless cantilevers are 

brought into contact with liquid layers or drops, the cantilever is often 

enveloped by the fluid. In this respect the use of a colloid probe can help 

prevent wetting of the cantilever beam and the associated degradation of 

the laser signal. 

Figure 9.11(a) shows a colloid probe attached to the tip of a V-shaped 

cantilever supported underneath the dimension scanner. In this example, 

no optical filters are used as careful alignment of both the optical microscope 

and the focal point of the laser reduces the transmission of diffuse 

laser light to the camera; although diffuse reflections are apparent (on the 

right hand side of the image), they are not excessive. If the observation 

angle is varied, such that the cantilever is viewed slightly from above, 

then either (i) optical filters are used or (ii) the field of view of the microscope 

is adjusted to omit all but the tip of the cantilever (under the same 

illumination conditions, omission of the optical filters permits higher 

photographic recording rates). This method is not employed using a light 

intesified system as the intensifier could be irreparably damaged. Figure 

9.11(b) shows the interaction between a 15-�m diameter colloid probe 

and a ‘large’ droplet of silicon oil, which is spread upon a reflective silica 

substrate. When first brought into contact, the silicon oil immediately 

enveloped the sphere and also adhered to the underside of the cantilever 

even though the cantilever was far above the surface of the drop; this 

effect was not readily apparent from above (as observed via the integrated 

AFM optics). The image shows the non-ideal liquid geometry during the 

(a) (b) 

FIguRE 9.11 (a) A colloid probe attached to the end of a V-shaped cantilever as 

observed using the optical system shown in Figure 9.9. The cantilever is observed directly 

from the side, hence the V-shape is not apparent. (b) The partial envelopment of a 15-�m 

diameter colloid probe by an excess of silicon oil (� � 12 Pa s).


late stages of separation of the surfaces, i.e. the liquid bridge is in contact 

with both the probe and the cantilever. 

Figure 9.12 shows the typical results obtained when attempting to generate 

a micro-CaBER experiment by the separation of a colloid probe and 

a flat surface coated with PDMS silicon oil. In this case, the size of the 

FIguRE 9.12 Selected frames documenting the thinning of a liquid bridge formed by 

the microscale separation of surfaces.


sphere and the thickness of the fluid layer are such that only the underside 

of the colloid is wetted. In frame 01, meniscus effects can be seen, 

when the surfaces are separated, a microscale liquid bridge is formed, 

which persists at large separations. The liquid bridge thins until the filament 

fails between frames 07 and 08, leaving residual liquid on both the 

probe and the lower surface. The evolution of the filament profile closely 

resembles the macroscale CaBER results shown in Figure 9.7. 

Figure 9.13 shows the behaviour of a thin liquid film during the ‘highspeed’ 

separation of the surfaces. In this instance, the high rates of separation 

and the high stress invoked in the fluid initially resist separation of the surfaces. 

Ultimately, the confined liquid layer appears to yield spontaneously 

(frame 02), forming a residual filament (initially 10-�m long and 1.3-�m in 

diameter created at an apparent rate � 5000 �m s�1 . The liquid filament then 

thins and breaks, residual liquid can be observed in frame 04. 

The adaptation of an AFM to act as a microrheometer has several 

potential benefits. In conventional rheometry, the generation of high 

rates of deformation is difficult, particularly so in extensional flow techniques 

where the defining strain rate is approximated by the relationship 

�ε � . U/h. The uniaxial rate of extension of cylindrical filaments between 

separating surfaces is equal to the ratio of the separation velocity U and 

the instantaneous length of the filament h. 

FIguRE 9.13 The high-speed separation of surfaces bridged by a thin film of silicon oil 

(� � 12 Pa s). Frame interval is 2 m s.


Therefore when the initial surface separation distance h is large, i.e. the 

initial characteristic length of the fluid sample is �1 mm, the attainment 

of moderate extensional rates (�100 s �1 ) requires an initial separation 

velocity � 100 mm s �1 , which is readily achieved using linear drive systems. 

However, the filament length must increase exponentially as a function 

of time in order to maintain a constant rate of extension, a situation 

which most drive systems are unable to accommodate. Consequently, 

many tensile studies involving liquids are restricted to low rates of extension 

(�10 s �1 ) or small total strains. In this respect, the recreation of elongational 

flows at the mesoscale using piezoceramic technology presents 

one possible method by which high extensional strain rates and large total 

strains may be achieved. Furthermore, the difficulties encountered when 

attempting to measure rapidly changing, small tensile forces, which are 

generated within low viscosity, liquid filaments may also be addressed by 

utilising the precise force measuring capabilities of the AFM. 

The determination of tensile forces in flows which contain a dominant 

elongational component is readily achieved using an AFM force sensor; 

however, the ability to precisely determine elongational stress at large 

strains is only possible when the shape and size of the liquid layer is 

clearly understood. In this respect, it is necessary to document the evolution 

of a microfilament to ascertain the minimum diameter such that the 

maximum tensile stress may be calculated. This is particularly important 

as the transient evolution of the profile of Newtonian and non-Newtonian 

liquid bridges may vary significantly such that a representation of the 

tensile stress through terms such as F/R 2 may not be valid at large separations. 

This is because the critical dimension (i.e. the filament diameter) is 

not simply related to separation distance and is itself dependent upon the 

viscoelastic properties of the material. 

The ability of many fluid mechanical systems to perform the desired 

function is critically dependent upon the tensile properties of the material, 

and the inability of the fluid to sustain large tensions is often beneficial, 

e.g. in coating and lubricating flows. Characterisation of the shear, extensional 

and cavitational behaviour is clearly important, and the ability of 

an AFM to recreate high-rate deformations which are comparable to those 

encountered in industrial processes is of particular interest. Moreover, the 

ability to experimentally recreate film splitting, fibrillation and cavitational 

cohesive failure in one dynamic process is desirable. However, observation 

of rapid microscale phenomena is not straightforward, especially so 

when cavitational mechanisms are encountered, as the observation of the 

growth and collapse of vapourous cavities requires microsecond temporal 

resolution. Future work will extend the capabilities of the AFM–optical 

microscopy system to further investigate the presence and influence of cavitational 

effects prior to the apparent cohesive failure of lubricant layers. As 

such, it is necessary to evolve the design of the experiment and in the first

LIST OF SyMbOLS 269 

instance it is intended to conduct additional microscopic observations from 

beneath the liquid layer. In this way, the current restrictions imposed by the 

focal distance can be reduced (it is necessary to use ULWD dry lenses to 

document filament formation), and high numerical aperture oil immersion 

lenses may be employed to study microscale cavitational effects in the thin 

fluid layer prior to the mesoscale deformation process. 

ACknowLEDgEMEnTS 

The authors would like to acknowledge Prof. W. Richard Bowen and 

Prof. Nidal Hilal for their significant contribution to the research content 

presented in section 9.6. The authors are grateful for the financial support 

of the EPSRC, the work reported here was conducted under EPSRC grant 

no. GR/S10438/01. 

LIST oF SyMBoLS 

A Cantilever vibration amplitude m 

an Constant 

B Geometric apparatus coefficient m 

bp Viscous damping coefficient N s m�1 F Force N 

G* Complex modulus Pa 

G’′ Elastic modulus Pa 

G“″ Viscous modulus Pa 

H Separation distance between probe and surface m 

K Spring constant N m�1 R Radius of sphere m 

T Cantilever thickness m 

U Relative separation velocity m s�1 X Cantilever width m 

Z Displacement m 

� Ratio of cantilever and drive amplitude 

�circ Hydrodynamic function for cylindrical cantilever 

�rect Hydrodynamic function for rectangular 

cantilever 

� Rheological phase angle °


ε Shear strain 

� Shear viscosity Pa s 

� Exponential damping length m 

� Mass per unit length of cantilever kg m �1 

� c Cantilever density kg m �3 

� fluid Fluid density kg m �3 

� Shear stress N m �2 

φ Phase difference between substrate and cantilever ° 

� Frequency 

� R 

� vacuum 

Resonant frequency 

Resonant frequency in vacuum 

� Correction factor 

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[92] R. Vorreuther, R. Corleis, T. Klotz, P. Bernards, U. Engelmann, Impact of shock wave 

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[93] P. Zhong, I. Cionta, S. Zhu, F.H. Cocks, G.M. Preminger, Effects of tissue constraint 

on shock wave-induced bubble expansion in vivo, J. Acoust. Soc. Am. 104 (1998) 

3126–3129.

C H A P T E R 

10 

Future Prospects 

The preceding chapters have shown that the use of AFM has already 

made substantial contributions to understanding and improving processes 

across a wide range of engineering. The literature on such applications is 

very extensive, so the aim of the present book has been to focus on some 

key examples in depth rather than to attempt a comprehensive overview, 

which would necessarily have been either unreasonably lengthy or else 

unsatisfyingly superficial. It is our hope that we have given an account of 

the principles, achievements and possibilities of AFM that is sufficiently 

informative for experts in other areas of process engineering to envisage 

how their own work may be enhanced using the techniques described. 

Owing to the broadness of the field, it is difficult to envisage where the 

most important developments are likely to take place in the future. However, 

we have asked the authors of the preceding chapters to give a brief 

account as to how they would see the use of AFM in their own specialties 

developing, with the following results. 

The importance of AFM lies in its capability to provide better understanding 

of materials’ structure, surface characteristics and the interactive 

forces at the meso- and nanoscale level. This will greatly help understand 

large-scale engineering processes, especially as materials are increasingly 

being designed down to the submicrometre level. The developments of 

colloid, coated-colloid and cell probe techniques have already opened 

new windows of applications to a variety of engineering processes including 

those involving bubbles, such as flotation, and processes within the 

biotechnology sector. For example, characterisation of membrane surface 

morphology and forces of interaction with colloidal particles and cells 

has facilitated the development of synthetic membranes with greatly 

improved process-separation characteristics. As synthetic membranes play 

a key role in water treatment, including desalination, such use of AFM is 

likely to be an increasingly important application. Similarly, AFM studies 

of particle-bubble interactions can play a major role in optimising mineral 

separations, one of the largest-scale of all process operations. However, 



276 10. FuTuRE PRosPECTs 

most AFM studies have so far been carried out under ambient conditions, 

whereas many industrial processes operate at reduced or elevated temperatures 

and pressures. The more recent development of hot–cold stages 

has made possible the application of AFM for both imaging and quantification 

of forces of interactions in the temperature range between �90°C 

and 250°C. Future development of pressure cells to enable the operation 

at both vacuum and pressures higher than atmospheric will further widen 

the range of process-relevant environments for further studies. 

The application of process engineering knowledge to biotechnology 

and medicine is showing huge potential. The integration of cutting-edge 

techniques to develop tailored cellular micro-environments as model 

systems has proven essential for the systematic investigation of a number 

of physiological processes in cell biology. From these studies, it has 

become apparent that restoring native functionalities using smart extracellular 

matrix (ECM), or tissue, depends on adequate consideration of 

interconnected processes that are regulated by biochemical, physical and 

mechanical factors in the ECM. 

AFM, with its proven capability for nanoscale measurements of biomolecular 

interactions, and physical and mechanical properties of materials, 

is expected to continue to make invaluable contributions to cell biology 

and biotechnology fields. However, new developments are desirable 

to improve measurement reliability and to understand the factors that 

determine measurement reproducibility. In the same way as closed-loop 

scanners have greatly enhanced the metrological capabilities of AFM and 

hence the precision in measurement of large biological samples (such as 

living cells), there is still much scope for improvements associated with 

force measurements. This may be in the area of probe fabrication, providing 

cheap sources of cantilevers with high-tolerance spring constants or more 

likely in reliable, accurate, non-destructive and (hopefully) simple protocols 

for the calibration of existing probe types. Such improvements may 

in turn provide an impetus for the development and widespread use of 

mathematical modelling (such as the use of finite element techniques) to 

interpret force curves in the context of heterogeneous cellular structures – 

modern computing now makes such data fitting a tractable problem. Such 

approaches require close collaboration between biologists, engineers and 

physical scientists. 

The integration of AFM and optical techniques for simultaneous interrogation 

of biochemical functionalities with physical/mechanical properties 

of a cell offers huge benefits and is likely to attract increasing research 

efforts. High-speed optical imaging offers the possibility of monitoring 

processes that are currently too fast for AFM to interrogate. The present 

developments of high-speed AFM imaging are certainly encouraging. 

However, progress is required to minimise the tip-surface interactions 

that, at these speeds, greatly perturb the surface being imaged.

10. FuTuRE PRosPECTs 277 

In recent years, a number of complementary measurement probes have 

been integrated onto AFM tips, permitting the imaging of other properties 

of a sample simultaneously with its topography. These novel developments 

have included the incorporation of electrochemical, thermal, magnetic and 

electronic sensors. Researchers have also found that, in addition to being 

able to perform measurement functions, often these sensors allow the 

controlled alteration of the local environment around the tip. Preliminary 

work using certain types of sensors has shown that this feature could find 

great applicability in modulating micro- and nanoenvironments of living 

cells. Such functionalised probes could be incorporated into an existing 

AFM system, hence significantly enhancing its capability at modest cost. 

The availability of high-quality probes is also a factor limiting the uptake 

of some combined techniques, such as AFM and scanning near field optical 

microscopy (SNOM). The combination of super-resolution optical and 

topographic imaging (AFM-SNOM) is certainly of great interest to biologists 

because of the wealth of new information it could provide. 

Polymers on surfaces play and will continue to play a major role in various 

engineering applications such as colloidal stabilisation, lab-on-a-chip 

devices, polymer composites and nanocomposites. Surprisingly, the significance 

of the polymer-solid interface region has been realised only relatively 

recently, and there are many gaps in our basic understanding. In nanocomposites, 

the interface regions can be so extensive that they can occupy most 

of the overall volume of the material even at low or moderate nanoparticle 

loadings. Furthermore, the conformation and nature of entanglements of 

confined polymer chains in close proximity to a solid surface can deviate 

significantly from the bulk. As AFM is a real-space, high-resolution surface 

technique capable of probing quantitatively both the nanostructural and 

nanomechanical properties, it is likely to play an important role in the study 

of the interface region in polymer composites and nanocomposites. 

The self-assembly and self-organisation of polymers on solid–liquid 

interfaces can be used as a generic technique for the inexpensive mass 

production of surface nanostructures and nanopatterns. Many issues 

remain to be elucidated by careful quantitative experimentation, and AFM 

is being proven to be an indispensable tool for the study of such systems 

in air or in liquids. Furthermore, the recent development of high-speed 

AFM with image-acquisition times in the order of a few milliseconds is an 

important development that could allow the monitoring of the mobility 

of polymer chains on a solid surface and consequently the kinetic paths 

of the nanostructures/nanopatterns formation. AFM offers the possibility 

for systematic studies of such systems that can elucidate the underlying 

physical mechanisms of the processes occurring on solid surfaces. These 

studies can lead in the construction of phase/state diagrams, which may 

be used for the design of well-controlled and specified surface nanostructures 

for applications spanning from nanoelectronic devices to vectors for

278 10. FuTuRE PRosPECTs 

targeted drug/gene delivery. Further, AFM is becoming an indispensable 

characterisation tool of miniaturised device components, which increasingly 

involve the use of (bio)polymers, ultrathin films and nanostructures 

on surfaces. 

To date, the successful use of AFM-based techniques to determine the 

viscoelastic properties of materials is exemplified by the successful use of 

indentation or compression experiments, for which established theoretical 

models adequately describe the rheological properties. Of particular 

note are the developments in biomechanical studies, wherein the determination 

of the viscoelastic response of cells and biological tissues using a 

combination of an AFM and a confocal laser scanning microscope (CLSM) 

is an interesting development, especially so with the use of modern fastscanning 

CLSMs. 

For fluids, although experimental studies have shown that an AFM is 

certainly capable of emulating the rheological capabilities of the surface 

forces apparatus (SFA), the use of an AFM to quantitatively describe the 

rheology of thin fluid films remains the subject of considerable research 

interest. Although, the viability of AFM as a micro-rheometrical tool 

has been established, the development of mathematical models capable 

of interpreting the response of microcantilevers in viscoelastic fluids is 

still evolving, and further development is vital to the successful application 

of this technique. Nevertheless, the integration of AFM cantilevers in 

microfluidic and other fluid sensor devices is a realistic option, enabled 

most significantly by advances in the description of viscous effects upon 

resonance characteristics. From a rheometrical perspective, this is particularly 

encouraging as few other technologies can address the associated 

issues of scale. The development of this area will in part rely upon the 

fabrication of appropriate cantilever geometries, such that the resonance 

characteristics and sensitivity of the device are optimized for the fluid of 

interest. In this respect, the fabrication of multilevers on common substrates 

may extend the measuring capabilities and represents a potential 

enabling technology for the study of more complex, multicomponent fluidic 

systems. 

The adaptation of dynamic AFM methods for the routine rheological 

characterisation of thin fluid films is more problematical. However, 

qualitative results suggest that the technique has potential merits. The 

dynamic response of a vibrating probe is clearly able to detect the onset 

of viscoelastic behaviour, but quantitative rheological information as yet 

remains elusive. Surprisingly, many dynamic studies favour oscillation 

in the direction normal to the surface, and as such it may be anticipated 

that significant compressional wave components can influence oscillation 

of the probe. For the analogous study of macroscale oscillatory shear 

and microscale rheometrical parameters, further studies on oscillatory 

microscale shear deformations would be beneficial.

10. FuTuRE PRosPECTs 279 

In either case, as the system response is not simply related to the stress 

and the strain in the fluid, there is at present no satisfactory way to quantitatively 

determine the complex moduli. However, the promising results 

of studies to date suggest that an AFM operating in dynamic mode is 

suited to adaptation as a mechanical interferometer, i.e. a device that can 

be used to determine the ‘time of flight’ of small amplitude shear waves 

across a fluid-filled gap. This is analogous to the so-called virtual gap 

rheometer (VGR), wherein the phase delays determined at two different 

locations in the fluid can be used to determine the phase velocity of the 

shear wave. By studying several frequencies, the frequency-dependent 

behaviour of viscoelastic systems may be exploited to determine the gel 

point of curing polymers. 

Most importantly, the future prospects of all applications of AFM in 

process engineering will be greatly enhanced by increased collaboration 

between engineers, physical scientists, biological scientists, mathematicians 

and instrument manufacturers. Among the most crucial of the multidisciplinary 

themes that need to be addressed are the development of probes of 

highly specified and reproducible physical properties; the development of 

high-speed image acquisition so that dynamic processes may be followed; 

the combination of AFM with other techniques in a single instrument, 

especially techniques that allow chemical characterisation of surfaces and 

the integration of AFM data acquisition and advanced mathematical 

modelling software for data interpretation.

A 

Actin stress fiber, 197 

Adhesion, 67–70, 198, 202, 226, 234, 246 

drug particles, 174–76, 178–79, 182, 184 

forces, 67–70, 81, 91–93, 97, 141–43, 

151–63, 164–66 

particles to bubbles, 83–85, 90, 91 

particles to membranes, 112, 113, 122 

Adhesives, 248–49 

AFM-optical microscope, 211 

Aggregation, 229, 236 

Apparatus coefficient, 255 

Arg-Gly-Asp (RGD), 197, 203–04 

Atomic force acoustic microscopy, 252 

B 

Biaxial extension, 248 

Biocompatibility, 226 

Biofilms, 135 

Block copolymer, 228, 236–237 

Boundary conditions, 49 

charge regulation, 49 

constant surface charge, 49 

constant surface potential, 49 

constant zeta potential, 49 

Bovine Serum Albumin (BSA), 49 

C 

Capillary forces, 10, 15, 18, 90, 94, 230 

Cauchy Plot, 41 

Cavitation, 246–47, 259–61 

Cell membrane, 197 

Collagen fibres, 205 

Cell model, 52 

Cell probe, 113 

Charging of surface, 44 

Chemisorption, 227 

Chloride ion binding, 51 

Coating flows, 247 

Colloid probe, 22–23, 32, 55, 69, 111, 112, 

210, 248, 253–55, 265–67 

coated, 113 

membrane measurements, 151–63, 164–66 

particle bubble measurements, 82, 91–93, 

96, 99 

Index 

281 

Colloidal gas aphrons, 95–97 

Colloidal lithography, 203, 207 

Cytoplasm, 197 

Cytoskeleton, 197, 212, 217 

Complex modulus, 252–53 

Confined fluids, 252–56, 259–67 

Contact angles, 88–91 

Contact mode, 9 

Convolution, 230–31 

Corrosion metal, 132 

Counterions, 47 

Critical flux, 123 

D 

Damping coefficient, 254–55 

Density, 247, 256–59 

Derjaguin approximation, 33 

Derjaguin, Muller Toporov model, 

67, 178 

Dewetting, 229, 236 

DLVO theory, 53–54, 154 

forces, 54–58, 91, 93 

DMT model, see Derjaguin, Muller Toporov 

model 

Dry powder inhalator, 174–76 

Dynamic AFM, 2, 10–11, 249–56 

E 

Effective stiffness, 43 

Elastic modulus, 180–81 

see also Young’s modulus 

Elasticity, 214 

Electrical double layer interactions, 47–53 

analytical solutions, 47 

numerical solutions, 48 

Electromechanical oscillator, 252 

Electron beam lithography (EBL), 203, 208 

Extracellular matrix (ECM), 195, 205 

proteins, 196, 197, 207 

Electropolishing, 130 

Electrostatic interactions, 111, 121, 227 

Entropic elasticity, 234 

Exponential damping length, 258 

Extensional flow, 261 

Extensional rheometer, 261

282 InDEx 

F 

Filamentation, 259, 261–62, 264–67 

Film splitting, 247, 267 

Filopodia, 198, 207, 212 

Focal adhesion, 197–8 

Focal complex, 198 

Force between two spheres, 33 

Force distance curve, 111, 112, 117 

Force map, 250 

Force modulation, 12, 249 

Force oscillations, 61 

Force volume imaging, 11 

Formulation, 174–75, 178, 182, 185–87, 

188–90 

Fourier transform, 256 

Friction force microscopy, 21, 248 

Frictional force mode, 12 

Frictional forces, 12, 63, 178–79, 248 

see also Lateral force 

Froth flotation, 82 

Functionalised surface, 199 

G 

Gouy-Chapman theory, 45–46 

Grafting density, 228, 231–233 

H 

Hamaker constant, 38–42 

calculation of, 40 

pairwise addition, 38 

Hardness, 180 

Hertz model, 12, 180–82, 214–7, 248 

High-speed video microscopy, 263 

Humic acid, 166 

Humic substances, 140 

Humidity, 175–77, 183, 186 

Hydration forces, 59–60 

Hydrodynamic drag, 66 

Hydrodynamic forces, 63, 84–85, 98–100 

Hydrodynamic function, 17, 257–58 

Hydrodynamic lubrication, 253–54 

Hydrophobic surfaces, 64 

I 

Imaging in liquid, 116, 123 

Indentation, 179–82, 215, 247, 251 

Inner Helmholtz plane (IHP), 46 

Integrins, 197 

Intermittent contact mode, see Tapping 

mode 

Isopotential lines, 119 

J 

JKR model, see Johnson, Kendall, Roberts 

model 

Johnson, Kendall, Roberts model, 12, 67, 

84, 178 

L 

Lamellipodia, 198 

Living cells, 212–4 

Lateral force, 12–22, 248–49 

Lateral resolution, 226 

Lennard-Jones potential, 36–37 

Lifshitz theory, 38, 40 

Light intensifier, 264–65 

Line tension, 89 

Liquid bridge, 255, 261, 265–68 

Liquid structure, 58–59 

Loading force, 234–35 

bubble, 97 

membrane, 151–60 

Loss modulus, 253 

M 

Macromolecules, 225, 229 

Membrane characterisation, 141 

Membranes, 57, 107–26 

development, 124–26 

fouling, 57, 68, 140–44 

Mesoscale, 246, 261 

Metal surfaces, 126 

Metastability, 260 

Microcontact printing, 201 

Micropatterning, 199 

Microsphere indentation, 210 

Microfilament, 264–67 

Microfiltration, 108 

Microfoams, 95–97 

Micromanipulator, 34 

Microrheometry, 247, 261–68 

Microsensor, 247 

Modification of filtration membranes, 

139–68 

Molecular weight cut-off, 113 

Monolayers, 226–30, 233–34, 236–39 

Multiparticle interaction, 52–53 

n 

Nanofiltration, 108 

Nanoimprint lithography (NIL), 203 

Nanopatterning, 203, 226–28, 233 

Nanotopography, 205–6

Natural organic matter, 140 

Negative pressure, 247 

Non-contact mode, 10–11 

Non-DLVO forces, 58 

O 

Optical microscope, 262, 264 

Outer Helmholtz plane (OHP), 46 

P 

Particle-bubble interactions, 81–106 

Pharmaceuticals, 173–90 

Phase angle, 250, 254–56 

Phase imaging, 10, 185–86 

Photolithography, 199 

Physisorption, 199 

Polymer demixing, 206 

Physisorption, 227, 230, 235 

Pinned micelles, 232 

Poisson-Boltzmann Equation, 45 

Polar liquids, 55 

Polymer brush, 228–36 

Polymer chains, 226–34, 237–41 

Polymer coatings, 225–26 

Pore size diameter, 115 distribution, 109, 

110, 116, 118, 119 

Pore size distribution, 140, 147–50, 168 

Powders, 174–75 

Primary alcohols, 61 

Q 

Q factor, see Quality factor 

Quality factor, 17 

R 

Resonance spectra, 256–59 

Resonant frequency, 17, 21, 258 

Retardation, 40 

Reverse osmosis, 108 

Reynolds number, 257 

Rheology, 246, 252–56, 262 

Roughness, 42, 44, 55, 69–70, 115, 120, 128, 

129, 134 

S 

Scanning probe lithography, 203 

Scanning thermal microscope, 186–90 

Self assembled monolayers (SAM), 199 

Self-assembly nanofabrication, 203 

SEM, 210 

InDEx 283 

Shear strain, 252, 255 

Shear stress, 252, 255 

Simple harmonic oscillator, 257 

Soft lithography, 201 

Solvation forces, 58–62 

Spring constant, 176–77 

Spring constant calibration, 16–22 

Spring constants, 87 

Star polymers, 237–240 

Steel, 132 

Steric interactions, 62 

Storage modulus, 253 

Stress fiber, 208 

Surface electrical properties, 117 

T 

Tack, 247, 249 

Tapping mode, 10, 236–37, 240, 250 

TEM, 210 

Tension, 246, 259–60 

Theta solvents, 62 

Thin liquid films, 254, 260 

Three-phase contact, 83, 88–90, 94–95, 97 

Threshold force, 94–95, 97 

Torsional spring constant, 21–22 

U 

Ultrafiltration, 108 

Uniaxial extension, 267 

V 

van der Waals forces, 35–44, 83–84, 

91, 227 

Debye forces, 35–37 

Keesom forces, 35–37 

London dispersion forces, 35–37 

Measurement by AFM, 42 

Viscoelasticity, 249, 252–53, 255, 259 

Viscosity, 247, 255–59 

W 

Work of adhesion, 43, 84 

Y 

Young equation, 88–89 

Young’s modulus (E), 180–82, 215, 247 

see also Elastic modulus 

Z 

Zeroth-order Stern model, 51

W. Richard Bowen and Nidal Hilal 4

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